Question

Find the vector of magnitude 14 in the direction of `vecQP`, where P and Q are the points (1, 3, 2) and (−1, 0, 8) respectively.

Answer 1

Points: P(1, 3, 2), Q(−1, 0, 8)

`vecQP = P - Q`

= (1 − (−1), 3 − 0, 2 − 8)

= (2, 3, −6)

Magnitude:

`vec(|QP|) = sqrt(2^2 + 3^2 + (-6)^2)`

= `sqrt(4 + 9 + 36)`

∴ `vec(|QP|) = 7`

Unit vector:

`vec(QP)/vec(|QP|) = (2hati + 3hatj - 6hatk)/7`

Required vector of magnitude 14:

`14((2hati + 3hatj - 6hatk)/7)`

= `2(2hati + 3hatj - 6hatk)`

= `(4hati + 6hatj - 12hatk)`

Hence, the vector of magnitude 14 is `(4hati + 6hatj - 12hatk)`.