Vectors Operations Quiz

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1. What has magnitude and direction?

Explanation

A vector has both magnitude and direction. Magnitude refers to the length or size of the vector, while direction indicates the orientation or angle at which the vector is pointing. Vectors are often represented by arrows, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction. Scalars, on the other hand, only have magnitude and do not have a specific direction associated with them. Therefore, the correct answer is vector.

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About This Quiz
Vectors Operations Quiz - Quiz

Do you know about vector operations? Take this vectors operations quiz to find out how much you know about this concept. Here, we have got a few questions to test your knowledge of vector operations. Give this quiz a try to see your level of understanding of vector operations. Try... see moreto get a 100% score on this quiz. If you find this quiz helpful in your practice of vector operations, do not forget to share it with others.
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2. Given u = <3, 7> and v =<-5, 4>, find 2u - 3v.

Explanation

To find 2u - 3v, we need to multiply each component of u by 2 and each component of v by -3, and then subtract the corresponding components.

For u = , multiplying each component by 2 gives us .
For v = , multiplying each component by -3 gives us .

Now, subtracting the corresponding components gives us = .

Therefore, the correct answer is .

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3. Given v = <3,-5> and w = <-2,3>, what is 2v + 3w?

Explanation

To find 2v + 3w, we need to multiply each component of v by 2 and each component of w by 3, and then add the corresponding components together.

2v = 2 * =
3w = 3 * =

Adding the corresponding components:
2v + 3w = + = =

Therefore, the correct answer is .

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4. If w = <2, -5> and y = <2, 0>, find 2w + y.

Explanation

The given question asks to find the value of 2w + y, where w = and y = . To find 2w, we multiply each component of w by 2, resulting in . Adding this to y, we get + = . Therefore, the correct answer is .

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5. If v =〈a,b〉, then a is the ___________ component of v.

Explanation

If v = ⟨a,b⟩, then a is the horizontal component of v. This is because in a two-dimensional Cartesian coordinate system, the x-axis represents the horizontal direction. The vector v = ⟨a,b⟩ represents a displacement in the x-axis (horizontal direction) of a units and in the y-axis (vertical direction) of b units. Therefore, a represents the displacement in the horizontal direction, making it the horizontal component of v.

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6. Find the magnitude of the vector <2, -3>.

Explanation

The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, the vector has a magnitude of √(2^2 + (-3)^2) = √(4 + 9) = √13. Therefore, the correct answer is √13.

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7. If a turtle moves from coordinate P = (3,2) to Q = (5,6). Which vector models the turtle's motion?

Explanation

The turtle moves from coordinate P = (3,2) to Q = (5,6). To find the vector that models the turtle's motion, we need to find the difference between the coordinates of Q and P. The x-coordinate of Q is 5 and the x-coordinate of P is 3, so the x-component of the vector is 5 - 3 = 2. Similarly, the y-coordinate of Q is 6 and the y-coordinate of P is 2, so the y-component of the vector is 6 - 2 = 4. Therefore, the vector that models the turtle's motion is .

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8. Find the angle between the two vectors <3, 4> and <4, -3>.

Explanation

The angle between two vectors can be found using the dot product formula. The dot product of two vectors A and B is given by A · B = |A| |B| cosθ, where |A| and |B| are the magnitudes of the vectors and θ is the angle between them. In this case, the dot product of and is 3*4 + 4*(-3) = 12 - 12 = 0. Since the dot product is 0, the angle between the two vectors is 90°.

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9. Find the component form of a vector whose magnitude is 10 and direction is 150°.

Explanation

The correct answer is "<-5√3, -5>". This is the component form of a vector with a magnitude of 10 and a direction of 150 degrees. The first component, -5√3, represents the horizontal displacement of the vector, and the second component, -5, represents the vertical displacement.

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10. Given vector u<-1,3,5> and v<3,y,z>, how much is y and z so the vectors are orthogonal.

Explanation

To determine if two vectors are orthogonal, their dot product must be equal to zero.
The dot product of u and v is given by -1(3) + 3(y) + 5(z).
Setting this expression equal to zero and solving for y and z, we get 3y + 5z = 1.
The only values of y and z that satisfy this equation are y = 6 and z = -3. Therefore, y = 6 and z = -3 make the vectors u and v orthogonal.

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What has magnitude and direction?
Given u = <3, 7> and v =<-5, 4>, find 2u - 3v.
Given v = <3,-5> and w = <-2,3>, what...
If w = <2, -5> and y = <2, 0>, find 2w + y.
If v =〈a,b〉, then a is the ___________ component...
Find the magnitude of the vector <2, -3>.
If a turtle moves from coordinate P = (3,2) to Q = (5,6). Which...
Find the angle between the two vectors <3, 4> and <4, -3>.
Find the component form of a vector whose magnitude is 10 and...
Given vector u<-1,3,5> and v<3,y,z>, how much is y and z...
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