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The two variables vectors 3xhati-yhatj-3...

The two variables vectors `3xhati-yhatj-3hatk and xhati-4yhatj+4hatk` are orthogonal to each other, then the locus of (x,y) is

A

hyperbola

B

circle

C

straight line

D

ellipse

Text Solution

Verified by Experts

The correct Answer is:
A
Since, `3xhati+yhatj-3hatk` and `xhati-4hatj+4hatk` are orthogonal
`(3xhati+yhatj-3hatk)*(xhati-4hatj+4hatk)=0`
`implies3x^(2)-4y^(2)-12=0`
`implies3x^(2)-4y^(2)=12implies(x^(2))/(4)-(y^(2))/(3)=1`
Its represent the equation of hypebola.
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