Question

Suppose A

= 2i − 3j − 2k , B

= i − j + 3k and C

= −5i + 3j + 2k , then

i. Find the angle between the vectors 2 A
+ C
and A
− 3 B
. [3]

ii. Determine a unit vector perpendicular to the plane of the vectors B
and C.
[2]

iii.Does the vectors A
, B
and C
form a triangle? [2]

iv. Find the direction cosines of the vector 4 B.

[4]

2. A particle moves along a curve whose parametric equations are given by
x = e
−t
, y = 3cos5t and z = 3sin5t, where t is the time. Find the magnitude of the
velocity and acceleration at t = 0.

Answer 1

Answer:

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