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The angles made by line having direction...

The angles made by line having direction ratios (3,5,4) with Y-axis

A

`pi/4`

B

`pi/6`

C

`pi/3`

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, DR's of a line are (3,5,4)
`therefore` DC's of a line are `(3/sqrt(50),5/sqrt(50),4/sqrt(50))" "[thereforesqrt(3^2+5^2+4^2)=sqrt(50)]`
We know that DC's of Y-axis are (0,1,0)
`therefore" "costheta=l_1l_2+m_1m_2+n_1n_2`
`therefore" "costheta=3/(sqrt50)xx0+5/sqrt(50)xx1+4/sqrt(50)xx0`
`=0+5/(5sqrt2)`
`rArr" "costheta=1/sqrt2rArrtheta=pi/4`
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