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The direction cosines of the vector 3hat...

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
Vector `A=3hati-4hatj+5hatk`, we know that, direction cosines of
`A=(3)/(sqrt(3^(2)+4^(2)+5^(2))),(-4)/(sqrt(3^(2)+4^(2)+5^(2))),(5)/(sqrt(3^(2)+4^(2)+5^(2)))`
`=(3)/(5sqrt(2)),(-4)/(5sqrt(2)),(1)/(sqrt(2))`
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