ECAT Maths XI : Chapter 6 Vectors (test 1)

The value of a such that vector A = 2i + aj + k and vector B = 6i − 3j are perpendicular is:

The direction cosines of the line joining the points (1, −3, 2) and (3, −5, 1) are: (a) (b) (c) (d)

The value of a such that vector A = 2i + aj + k and vector B = 6i − 3j + 2k are perpendicular is:

If vector A = i + 3j − 2k and vector B = 4i − 2j + 4k, then the value of (2A + B) · (A − 2B) is:

The angle between A = 4i − 2j + 4k and B = 3i − 6j − 2k is:

Find the projection of the vector 4i − 3j + k on the line passing through the points (2, 3, −1) and (−2, −4, 3).

Find the work done in moving an object along the vector r = 3i + 2j − 5k if the applied force is F = 2i − j − k.

A particle, acted upon by force 4i + j + 3k and 3i + j - k is displaced from the point (1, 2, 3) to the point (5, 4, 1). Find the work the particle

Find the work done in moving an object along a vector vec r = 3i + 2j - 5k if the apply force if vec F = 2i - j - k ?

Find the work done in moving an object along a straight line from (3, 2, -1) to (2,-1,2) in a force field given by vec F = 4i - 3j + 2k

A = 2i − 3j − k and B = i + 4j − 2k. Find (A + B) × (A − B).

The volume of the parallelepiped whose three edges are 𝐚 = j, 𝐛 = −i + 2j, and 𝐜 = 3k − i − j is:

Find the value of 'a' such that 2i - 3j + 4ki + 2j - k, ai + 4j + k are coplanar?

Find the value of 'b' so that 2i - 3ji + bj + k3i - k are coplanar?

If vec A = i - 2j - 3k , B=2i+j-k & vec C = i + 3j - 2k Find vec A ( vec B * vec C ) ?

Sure! I'll use the **A→** style from now on since it copies correctly into WordPress. Your question becomes: Let A→ = 3i − j − 4k,B→ = −2i + 4j − 3k, and C→ = i + 2j − k**. The magnitude of 3A→ − 2B→ + 4C→ is:

Let A→ = 3i − j − 4k, B→ = −2i + 4j − 3k, and C→ = i + 2j − k. The unit vector parallel to 3A→ − 2B→ + 4C→ is:

If A→ = 3i − j − 4k, B→ = −2i + 4j − 3k, and C→ = i + 2j − k, find (A→ × B→)(B→ · C→).

If A→ = 3i − j − 4k, B→ = −2i + 4j − 3k, and C→ = i + 2j − k, find (A→ × B→) × C→.

If A→ = 2i + j − 3k and B→ = i − 2j + k, find a vector of magnitude 5 perpendicular to both A→ and B→.