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If A=3hat(i)+4hat(j) and B=7hat(i)+24hat...

If `A=3hat(i)+4hat(j)` and `B=7hat(i)+24hat(j)`,find the vector having the same magnitude as B and parallel to A.

A

`5hati+20hatj`

B

`15hati+10hatj`

C

`20hati+15hatj`

D

`15hati+20hatj`

Text Solution

Verified by Experts

The correct Answer is:
D
`|B|=sqrt(7^(2)+(24)^(2))=sqrt(625)=25`
Unit vector in the direction of A will be `hatA=(3hati+4hatj)/(5)`
So required vector `=25((3hati+4hatj)/(5))=15hati+20hatj`
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