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A line segment (vector) has length 21 an...

A line segment (vector) has length 21 and direction ratios (2, -3, 6). If the line makes an obtuse angle with x axis, the components of the line (vector) are

A

`-27,18,54`

B

`27,-18,54`

C

`27,-18,-54`

D

`-27,-18,-54`

Text Solution

Verified by Experts

Let the components of line segment on axes are x,y and z.
So, `x^(2)+y^(2)+z^(2)=63^(2)`
Now, `(x)/(3)=(y)/(-2)=(z)/(6)=k`
`because(3k)^(2)+(-2k)^(2)+(6k)^(2)=63^(2)`
`k=+-(63)/(7)=+-9`
`therefore` Components are `(27,-18,54)` or `(-27,18,-54)`.
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