If a - x- - y- and b - y -x- - a-b - -5- then the locus of x- y is -

A×b = î amp;ĵ amp; k̂ x amp; y amp;0 y amp; x amp; 0 = 0î+ 0ĵ +(x^2 + y^2) k̂ | a×b | = x^2 + y^2 x^2 + y^2 =5 It is an equation of a circl ...

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Byju's Answer

Standard XII

Mathematics

Family of Planes Passing through the Intersection of Two Planes

If a = xî - y...

Question

If $\to a = x^i - y^j$ and $\to b = y^i + x^j, ∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣ = 5,$ then the locus of $(x, y)$ is :

Hyperbola

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Parabola

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Ellipse

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Circle

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Solution

The correct option is D Circle
$\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k x & - y & 0 y & x & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0^i + 0^j + (x^{2} + y^{2})^k$
$∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣ = x^{2} + y^{2}$
$x^{2} + y^{2} = 5$
It is an equation of a circle.

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Family of Planes Passing through the Intersection of Two Planes

Standard XII Mathematics

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If →a=x^i−y^j and →b=y^i+x^j,∣∣∣→a×→b∣∣∣=5, then the locus of (x,y) is :

The correct option is D Circle→a×→b=∣∣ ∣ ∣∣^i^j^kx−y0yx0∣∣ ∣ ∣∣=0^i+0^j+(x2+y2)^k ∣∣∣→a×→b∣∣∣=x2+y2 x2+y2=5 It is an equation of a circle.

If $\to a = x^i - y^j$ and $\to b = y^i + x^j, ∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣ = 5,$ then the locus of $(x, y)$ is :