Vector Algebra

Reviewed by Editorial Team

The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.

Learn about Our Editorial Process

| By Tanmay Shankar

Tanmay Shankar

Community Contributor

Quizzes Created: 491 | Total Attempts: 1,846,919

| Attempts: 988

Quiz Flashcard

Questions

Feedback

During the Quiz End of Quiz

Difficulty

Easy First Hard First Sequential

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

1/15 Questions
- 0
- 1
- 2
- 3

About This Quiz

This Vector Algebra quiz assesses skills in computing vector properties and solving vector-related problems. It includes questions on finding position vectors, unit vectors, and areas of triangles using vector methods, essential for learners aiming to master vector algebra concepts.

2.
- 0
- 1
- 3
- 4
Correct Answer

A. 0
3.
- 4
- 5
- 6
- 7
Correct Answer

A. 4
4.
- 4
- -4
- 5
- 6
Correct Answer

A. -4
5.

Write unit vector in the direction of the sum of vectors:
Correct Answer

A.
6.
Correct Answer

A.
7.

Write the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q (4, 1, — 2).
Correct Answer

A.

Explanation

The position vector of the midpoint of the vector joining two points can be found by taking the average of the corresponding coordinates of the two points. In this case, the midpoint of the vector joining P(2, 3, 4) and Q(4, 1, -2) can be found by taking the average of the x-coordinates, y-coordinates, and z-coordinates. Therefore, the position vector of the midpoint is [(2+4)/2, (3+1)/2, (4+(-2))/2] = [3, 2, 1].

Rate this question:

2
8.

Show that each of the given three vectors is a unit vector: Which of the following is true?
- All of these
Correct Answer

A. All of these

Explanation

The statement "All of these" means that each of the given three vectors is a unit vector. A unit vector is a vector with a magnitude of 1. Since the question states that all of the given vectors are unit vectors, it implies that each vector has a magnitude of 1, satisfying the definition of a unit vector. Therefore, the answer is correct.

Rate this question:
9.
- 5
- -5
- Both A & B
- 7
Correct Answer

A. Both A & B
10.
- -1
- 1
- -1.5
- 2
Correct Answer

A. -1.5
11.
Correct Answer

A.
12.

Using vectors, find the area of the triangle ABC with vertices A (1, 2, 3), B (2, -1, 4) and C (4, 5, -1).
Correct Answer

A.

Explanation

To find the area of a triangle using vectors, we can use the cross product of two vectors formed by the sides of the triangle. The magnitude of the cross product gives us the area of the parallelogram formed by the two vectors, and dividing it by 2 gives us the area of the triangle.

In this case, we can find the vectors AB and AC by subtracting the coordinates of the respective points. Then, we can calculate the cross product of AB and AC. Taking the magnitude of the cross product and dividing it by 2 gives us the area of triangle ABC.

Rate this question:
13.
Correct Answer

A.
14.

P and Q are two points with position vectors and respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.
Correct Answer

A.

Explanation

The position vector of point R can be found by using the external division formula. According to the formula, the position vector of R is given by (2Q + 1P) / (2+1). This means that we multiply the position vector of Q by 2, the position vector of P by 1, and then add them together. Finally, we divide the result by the sum of the ratios, which is 2+1 = 3.

Rate this question:
15.
- Points are collinear
- Form a right angle triangle
- Doesn’t form a right triangle
- None of these
Correct Answer

A. Form a right angle triangle