If there are two vectors given <br> vec(OA)=hat(i)+2 hat(j) and vec(OB)=4 hat(i)+p hat(k) <br> Then find the values of p for which /_AOB=cos^{-1} (1/5).

Elisabeth Wiley

Elisabeth Wiley

Answered question

2022-08-12

If there are two vectors given
O A = i ^ + 2 j ^     and     O B = 4 i ^ + p k ^
Then find the values of p for which A O B = cos 1 ( 1 5 )
Would someone please give me a hand on solving this?

Answer & Explanation

Trevor Copeland

Trevor Copeland

Beginner2022-08-13Added 21 answers

HINT:
Try to use Dot product rule.which is
A . B = | A | . | B | . c o s θ
Here,
A = i ^ + 2 j ^ , B = 4 i ^ + p k ^
| A | = 1 2 + 2 2 = 5     ,     | B | = 16 + p 2
θ = cos 1 ( 1 5 )
If you substitute everything in the formula I think you will get,
p = ± 8

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