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What is the angle between a vector vec A...

What is the angle between a vector `vec A = 4hati +3hatj +5hatk` and the x-axis ?

A

`cos^(-1)""((3)/(5))`

B

`cos^(-1)""((2sqrt(2))/(sqrt(5)))`

C

`cos^(-1)""((3)/(sqrt(5)))`

D

`cos^(-1)""((2)/(5))`

Text Solution

Verified by Experts

The correct Answer is:
B
`A = sqrt(4^(2)+3^(2)+5^(2))=sqrt(50)=5sqrt(2)`
The angle between `vec A` and x-axis is given by
`cos alpha =(A_(x))/(|A|)=(4)/(5sqrt(2))=(2sqrt(2))/(sqrt(5))`
`therefore alpha = cos^(-1)""((2sqrt(2))/(sqrt(5)))`
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