The equation ${{\bf{r}}^{\vec 2}} - 2{\rm{\;}}{\bf{\vec r}}\cdot{\bf{\vec c}} + h = 0,\left| {{\bf{\vec c}}} \right| > \sqrt h $, represent

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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The equation

{\mathbf{r}^{\vec 2}} - 2\mathrm{\;}\mathbf{\vec r}\cdot\mathbf{\vec c} + h = 0,\left| {\mathbf{\vec c}} \right| > \sqrt h

, represent

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Correct option: D

Sphere

Option D (Sphere) is correct because the given equation is a form of the sphere equation in vector form.

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\vec r\cdot\vec a = \vec r\cdot\vec b = \vec r\cdot\vec c = 0

\vec r,

\left[ {\vec a\vec b\vec c} \right],

\frac{{x - 3}}{2} = \frac{{y - 2}}{3} = \frac{{z - 1}}{{ - 1}}

\frac{{x + 3}}{2} = \frac{{y - 6}}{1} = \frac{{z - 5}}{3},

\mathbf{\vec a} = \widehat \mathbf{i} - \mathbf{\hat k},\;\mathbf{\vec b} = x\widehat \mathbf{i} + \widehat \mathbf{j} + \left( {1 - x} \right)\mathbf{\hat k}

\mathbf{\vec c} = y\widehat \mathbf{i} + x\widehat \mathbf{j} + \left( {1 + x - y} \right)\mathbf{\hat k}.

\left[ {\mathbf{\vec a},\;\mathbf{\vec b},\;\mathbf{\vec c}} \right]

\vec{a}, \vec{b}

((\vec{a} \times \vec{b}) \times \vec{a}) \cdot((\vec{b} \times \vec{a}) \times \vec{b})

a \cdot(a \times b)=

\mathbf{r}=\mathbf{b}+\lambda \mathbf{c}