Vectors: Angle between two vectors

Worked Solution:

The dot product (scalar product) of two vectors a and b is :

a.b = |a| |b| cos(α) where α is the angle between the vectors, and also
(p i + q j + r k).(t i + u j + v k) = p×t + q×u + r×v

cos(α) =

a.b |a| |b|

The two vectors in this question have lengths

|

–6 i + 8 j – k

| =

10.04988

and

|

–4 i – 3 j + 7 k

| = 8.60233

The dot product of the two vectors is (–6)×(–4) + 8×(–3) + (–1)×7 = –7

cos(α) =

–7 10.04988×8.60233

= –0.081

to 3 dps.

Since the angle and its cosine can be measured clockwise or anticlockwise, the answer 0.081 is also correct.