If the vectors -2 x -3 y k- and -3 x -2 y k- are orthogonal to each other- then the locus of the point x - y isA- A circleB- an ellipseC- a parabolaD- a straight line

The correct option is A A circleIt is given that the vectors î 2x ĵ 3yk̂ and î + 3x ĵ + 2y k̂ are orthogonal. Therefore, (î 2xĵ 3y k̂ ). (î + 3x ĵ + 2y ...

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Standard XII

Mathematics

Linear Combination of Vectors

If the vector...

Question

If the vectors $^i - 2 x^j - 3 y^k a n d^i + 3 x^j + 2 y^k$ are orthogonal to each other, then the locus of the point (x, y) is

A circle

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an ellipse

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a parabola

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a straight line

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Solution

The correct option is A A circle
It is given that the vectors $^i - 2 x^j - 3 y^k a n d^i + 3 x^j + 2 y^k$ are orthogonal. Therefore, $(^i - 2 x^j - 3 y^k) . (^i + 3 x^j + 2 y^k) = 0$ $\Rightarrow 1 - 6 x^{2} - 6 y^{2} = 0$ Which is a circle

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If the vectors ^i−2x^j−3y^k and ^i+3x^j+2y^k are orthogonal to each other, then the locus of the point (x, y) is

The correct option is A A circleIt is given that the vectors ^i−2x^j−3y^k and ^i+3x^j+2y^k are orthogonal. Therefore, (^i−2x^j−3y^k).(^i+3x^j+2y^k)=0 ⇒1−6x2−6y2=0 Which is a circle

If the vectors $^i - 2 x^j - 3 y^k a n d^i + 3 x^j + 2 y^k$ are orthogonal to each other, then the locus of the point (x, y) is

The correct option is A A circle
It is given that the vectors $^i - 2 x^j - 3 y^k a n d^i + 3 x^j + 2 y^k$ are orthogonal. Therefore, $(^i - 2 x^j - 3 y^k) . (^i + 3 x^j + 2 y^k) = 0$ $\Rightarrow 1 - 6 x^{2} - 6 y^{2} = 0$ Which is a circle