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A line passes through the points (6,-7,-...

A line passes through the points `(6,-7,-1) and (2,-3,1)` Find the direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.

A

`2/3,-2/3,-1/3`

B

`-2/3,2/3,1/3`

C

`2/3,-2/3,1/3`

D

`2/3,2/3,1/3`

Text Solution

Verified by Experts

The correct Answer is:
A
Let l,mm and n be the DC's of given libne Since line makes an acute angle with X-axis therefore `lgt0`. As the line passes through (6,-7,-1) and (2,-3,1), thereforeits DR's are
(6-2,-7+3,-1-1)
or (4,-4,-2)
or (2,-2,-1)
`thereforeDC` of the given line are `(2/3,-2/3,-1/3)`
`[thereforesqrt(2^2+(-2)^2+(-1)^2)=sqrt9=3]`
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