Online Test For Scalars And Vectors

A vector quantity is a type of quantity that has both magnitude and direction. This means that it not only represents a numerical value (magnitude) but also indicates the orientation or position in space (direction). Examples of vector quantities include velocity, force, displacement, and acceleration. These quantities require both magnitude and direction to fully describe their characteristics and cannot be represented by just a numerical value or just a direction alone. Therefore, option d) specifies both a magnitude and a direction, making it the correct answer.

Speed and velocity are both measures of how fast an object is moving, but they differ in that velocity also includes information about the direction of motion. Speed is a scalar quantity, meaning it only has magnitude (the numerical value) and no direction. On the other hand, velocity is a vector quantity, meaning it has both magnitude and direction. So, while speed tells us how fast an object is moving, velocity tells us both how fast it is moving and in which direction it is moving.

A scalar quantity is a type of measurement that is completely described by its magnitude, or size, and does not have a direction associated with it. This means that it does not involve any specific units or measurements of mass, as mentioned in option a. Option c is incorrect because scalar quantities do not show direction, unlike vector quantities. Therefore, the correct answer is b) is a quantity that is completely specified by its magnitude.

Explanation: A zero or null vector is a vector that has zero magnitude and an arbitrary direction. The velocity vector of a stationary object is a zero vector.

Force is an example of a vector quantity because it has both magnitude and direction. In physics, a vector quantity is defined as a quantity that has both magnitude and direction. Force is a vector quantity because it not only represents the amount of push or pull applied to an object (magnitude), but also the direction in which the force is applied. This is in contrast to scalar quantities, such as mass or density, which only have magnitude and no specific direction.

Volume is an example of a scalar quantity because it only has magnitude and no direction. Scalar quantities are described by their magnitude alone, without any reference to direction. Velocity, acceleration, and force, on the other hand, are vector quantities as they have both magnitude and direction.

To find the dot product of two vectors, we multiply their corresponding components and then add them together. In this case, a.b = (3 * 2) + (-1 * 1) + (0 * 4) = 6 - 1 + 0 = 5. Therefore, the dot product of vectors a and b is 5.

A unit vector is a vector that has a magnitude of 1. Therefore, the magnitude of a unit vector is unity.

When a coolie walks on a horizontal platform with load on his head, he applies force in the upward direction equal to its weight. The displacement of the load is along the horizontal direction. Thus the work done by the coolie on the load is zero.

Speed is defined as the magnitude of velocity, which means it only considers the magnitude or size of the velocity vector. Since speed only considers the magnitude, it cannot be negative as it represents the distance traveled per unit of time. Therefore, the statement that "speed can be negative" is not true.

When the boy pushes against the wall with 50 pounds of force, the wall exerts an equal and opposite force of 50 pounds on the boy according to Newton's third law of motion. Since the wall does not move, it means that the forces are balanced. The resultant force is the sum of all the forces acting on an object, and in this case, it is zero pounds. Therefore, the correct answer is c) 0 pounds.

The dot product is used to calculate the work done of vectors force F and distance d separated by angle θ. The dot product of two vectors gives the magnitude of one vector multiplied by the magnitude of the projection of the other vector onto the first vector. In this case, the dot product of force F and distance d gives the magnitude of the force multiplied by the component of the distance in the direction of the force, which represents the work done. Therefore, the correct answer is b) Dot product.

The resultant force can be found by subtracting the force towards south from the force towards north. Therefore, the resultant force is 20 N - 12 N = 8 N towards north.

The given vectors (-2,1,-1) and (0,3,1) are not parallel because parallel vectors have the same direction or are in the same line. In this case, the two vectors have different directions as their components are not proportional to each other. Therefore, the correct answer is c) Not parallel.

Explanation: While walking, a person presses the ground with his feet slightly slanted in the backward direction. The ground exerts upon him an equal and opposite reaction. Its horizontal component enables the person to move forward while the vertical component balances this weight.

For a body moving in a circular path, the centripetal force and the displacement are perpendicular to each other. So the work done by the centripetal force is zero.

The cross product of two vectors is a vector that is perpendicular to both of the original vectors. To find the cross product, we can use the formula: A x B = (AyBz - AzBy)i + (AzBx - AxBz)j + (AxBy - AyBx)k In this case, A = 3i + 4j - 5k and B = -i + j - 2k. Plugging in the values, we get: A x B = ((4)(-2) - (-5)(1))i + ((-5)(-1) - (3)(-2))j + ((3)(1) - (4)(-1))k = (-8 + 5)i + (5 + 6)j + (3 + 4)k = -3i + 11j + 7k Therefore, the correct answer is b) -3i + 11j + 7k.

The man initially walks 3 miles north, which means he is moving in a direction that is directly opposite to the south. Then, he turns right and walks 4 miles east. The resultant displacement is the straight line distance from the starting point to the ending point. Since the man walks 3 miles north and then 4 miles east, the resultant displacement is a right-angled triangle with sides of 3 miles and 4 miles. Using the Pythagorean theorem, we can calculate the hypotenuse, which is the resultant displacement. The square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the square of the hypotenuse is 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us 5. Therefore, the resultant displacement is 5 miles, and since the man is moving north and east, the direction is northeast.

When two vectors have a resultant equal to either, it means that the magnitude of the resultant vector is equal to the magnitude of each individual vector. In order for this to happen, the vectors must be equal in magnitude and opposite in direction. The angle between two vectors that are equal in magnitude and opposite in direction is 180°. However, since the options only include angles less than 180°, the closest option is 120°.

The work done by the gardener can be calculated using the formula: work = force x distance x cos(angle). In this case, the force applied is 20kg weight, which can be converted to Newtons by multiplying it with the acceleration due to gravity (9.8m/s^2). The distance covered is 20m. The angle between the force and the direction of motion is 60 degrees. Plugging in these values into the formula, we get: work = (20kg x 9.8m/s^2) x 20m x cos(60 degrees) = 1960J.

In scalar, the addition and subtraction operations are only performed on numbers according to their units. This means that the units of the numbers being added or subtracted must be the same. This is because scalar quantities only have magnitude and no direction, so the units play a crucial role in determining the validity of the operation. Therefore, the correct answer is c) Number according to unit.

The work done by a person is equal to the force applied multiplied by the distance moved in the direction of the force. In this case, the person applies a force of 10N and moves a horizontal distance of 5m, so the work done in the horizontal direction is 10N * 5m = 50J. The person then climbs up a vertical distance of 10m, but since the force is perpendicular to the displacement, no work is done in the vertical direction. Therefore, the total work done by the person is 50J.

The dot product of two vectors results in a scalar value, so option c) is not true.

The resultant magnitude of two vectors can never be negative because magnitude represents the size or length of a vector, which is always a positive quantity. The addition of two vectors can result in a vector with a magnitude of zero if they cancel each other out, but it cannot be negative.