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

|

–3 i – j – 6 k

| =

6.78233

and

|

5 i + 7 j + 9 k

| = 12.4499

The dot product of the two vectors is (–3)×5 + (–1)×7 + (–6)×9 = –76

cos(α) =

–76 6.78233×12.4499

= –0.900

to 3 dps.

Since the angle and its cosine can be measured clockwise or anticlockwise, the answer 0.900 is also correct.