Vector Algebra — Practice

Question 1

The unit vector in the direction of a = 3i − 4j + 12k is

Accepted Answer

A

Question 2

If a vector a = i + 2j + 2k makes direction cosines (l, m, n) with the coordinate axes, then (l, m, n) equals

Accepted Answer

A

Question 3

Two vectors of magnitudes 6 and 10 act at a point with an angle of 60° between them. The magnitude of their resultant is

Accepted Answer

A

Question 4

The position vectors of the vertices of triangle ABC are a = 2i+3j+4k, b = 4i−j+2k and c = 4j+6k. The position vector of the centroid of the triangle is

Accepted Answer

A

Question 5

The position vectors of points A and B are a = i+2j+3k and b = 6i−3j+8k. The position vector of the point P that divides AB internally in the ratio 2:3 is

Accepted Answer

A

Question 6

For what value of λ are the vectors a = 2i + λj + k and b = i − 2j + 3k perpendicular to each other?

Accepted Answer

A

Question 7

The cosine of the angle between the vectors a = i+2j+2k and b = 2i+2j+k is

Accepted Answer

A

Question 8

The scalar projection of a = 3i − j + 2k on b = i + 2j − 2k is

Accepted Answer

A

Question 9

The position vectors of the vertices of a triangle are a = i+j+k, b = 2i+3j+k and c = 3i+j+2k. The area of the triangle is

Accepted Answer

A

Question 10

A unit vector perpendicular to both a = i+j+k and b = 2i−j+2k is

Accepted Answer

A

Question 11

The volume of the parallelepiped whose coterminous edges are a = 2i−j+k, b = i+2j−k and c = i−j+2k is

Accepted Answer

A

Question 12

The vectors a = 2i − 4j + 6k and b = i − 2j + mk are parallel for m equal to

Accepted Answer

A

Practice — Vector Algebra

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