The locus of the point rcos-cos- rcos-sin- r sin- where - are variables and r is a constant is

The correct option is A x^2+y^2+z^2=r^2 Let x = rcos α cos β y = #160;rcos α sin β z = rsin α x^2 + y^2 = r^2cos^2α x^2 + y^2 + ...

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Applications of Dot Product

The locus of ...

Question

The locus of the point $(r cos α cos β, r cos α sin β, r sin α)$ where $α, β$ are variables and $r$ is a constant is

x + y + z = r

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x^{2} + y^{2} + z^{2} = r^{2}

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x^{2} + y^{2} + z^{2} = r

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x^{2} + y^{2} - z^{2} = r^{2}

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x = r cos α cos β

y = r cos α sin β

z = r

sin α

x^{2} + y^{2} + z^{2}

x^{2} + y^{2} + z^{2} = r^{2}

x^{2} + y^{2} - z^{2} = r^{2}

x^{2} - y^{2} + z^{2} = r^{2}

z^{2} + y^{2} - x^{2} = r^{2}

If $x = r s i n α c o s β, y = r s i n α s i n β$ and $z = r c o s α$ , then

u = f (r)

r^{2} = x^{2} + y^{2} + z^{2}

\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} + \frac{\partial^{2} u}{\partial z^{2}} = f^{''} (r) + \frac{2}{r} f (r)

x^{2} + y^{2} + z^{2} = 5, x, y, z \in R,

(x - y)^{2} + (y - z)^{2} + (z - x)^{2}

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