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The direction cosines of the vector 3hat...

The direction cosines of the vector `3hati-4hatj+5hatk` are

A

`(3)/(5),(-4)/(5),(1)/(5)`

B

`(3)/(5sqrt(2)),(-4)/(5sqrt(2)),(1)/(sqrt(2))`

C

`(3)/(sqrt(2)),(-4)/(sqrt(2)),(1)/(sqrt(2))`

D

`(3)/(5sqrt(2)),(4)/(5sqrt(2)),(1)/(sqrt(2))`.

Text Solution

Verified by Experts

The correct Answer is:
B
`r=3hati-4hatj+5hatk`
`implies |r|=sqrt(3^(2)+(-4)^(2)+5^(2))=5sqrt(2)`
Hence, direction cosines are `(3)/(5sqrt(2)),(-4)/(5sqrt(2)),(5)/(5sqrt(2))`
i.e., `(3)/(5sqrt(2)),(-4)/(5sqrt(2)),(1)/(sqrt(2))`.
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