JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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Analyzing +4 | -1

Let

\mathbf{r}=(\mathbf{a} \times \mathbf{b}) \sin x+(\mathbf{b} \times \mathbf{c}) \cos y+(\mathbf{c} \times \mathbf{a})

, where

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

are non-zero non-coplanar vectors. If

\mathbf{r}

is orthogonal to

3 \mathbf{a}+5 \mathbf{b}+2 \mathbf{c}

, then the value of

\sec ^2 y+\operatorname{cosec}^2 x+\sec y \operatorname{cosec} x

View answer and explanation

Correct option: A

Option A (3) is correct because substituting

\sin x = -1

and

\cos y = -1

into the expression

\sec^2 y + \csc^2 x + \sec y \csc x

yields 3.

More Questions from SCALAR TRIPLE PRODUCT

Practice All Chapter MCQs →

\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}