Question

If vector A dot vector B = root 3 (vector A cross vector B) what is the angle between vector A and vector B ?

Answer 1

If cross product and dot product of any two vectors is same then :

The angle between the vectors is 45° .

Because:

Cos ø = ( A.B )/ |A| |B|

Sin ø =( A x B )/ |A| |B|

We know that A.B = A x B

Therefore, Cos ø= Sin ø

Cos ø = Cos(90-ø)

Ø = 90- Ø

2 Ø = 90

Ø = 45°.

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Answer 2

Answer: 30°

Explanation:

Since a.b= ab cosΦ

And a X b = ab sinΦ

So, we get 1/root 3= ab sinΦ divided by ab cosΦ

Therefor 1/root 3= tanΦ

So Φ= 30° or π/6