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Given vec(A)=2hat(i)+phat(j)+qhat(k) and...

Given `vec(A)=2hat(i)+phat(j)+qhat(k)` and `vec(B)=5hat(i)+7hat(j)+3hat(k)`. If `vec(A)||vec(B)`, then the values of p and q are, respectively,

A

`14/5and6/5`

B

`14/3 and 6/5`

C

`6/5 and 1/3`

D

`3/4 and 1/4`

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(A)xxvec(B)=|(hat(i), hat(j), hat(k)) ,(2,p,q), (5,7 ,3)|=0`
or `hat(i)(3p-7q)+hat(j)(5q-6)+hat(k)(14-5p)=0`
`3p=7q,5q-6=0` or `q=6/5`
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