Question

two vectors p and q of equal magnitude make an angle 64 with each other what is the angle made by p-q vector with p

Answer 1

Answer:

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Answer 2

Answer:

The angle made by (p-q) vector with p is, 58 degrees.

Explanation:

Let the angle between the two vectors p and (p-q) be x.

Now, $|p-q|^{2}$ = $|p|^{2} + |q|^{2} - 2|p||q|cos64$

                 = $2|p|^{2} -2|p|^{2} cos64$

                 = $4|p|^{2} (sin32)^{2}$

Therefore, $|p-q|$ = $2|p|sin32$

Now, we need to find the angle formed between p-q vector and p vector.

$(p-q).p = |p-q||p|cosx \\= > |p|^{2} - |p|^{2} cos64 = 2|p|^{2} sin32cosx\\= > 2(sin32)^{2} = 2sin32cosx\\= > cosx = sin32 \\= > cosx = cos (\frac{\pi }{2} -32)\\= > x = 58$

Hence, the angle made by (p-q) vector with p is, 58 degrees.