JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

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Analyzing +4 | -1

\mathbf{u}, \mathbf{v}

and

\mathbf{w}

are non-coplanar vectors and

p, q

are real numbers, then the equality

[3 \mathbf{\,u\,} p\, \mathbf{v\,} p \mathbf{\,w}]-[p\, \mathbf{v\,} \mathbf{w\,} q\, u]

- [2w qv qu]

=0

holds for

View answer and explanation

Correct option: D

exactly one value of

(p, q)

Option D (exactly one value of

(p, q)

) is correct because the equation simplifies to

3p^2 - pq + 2q^2 = 0

, which has only one solution:

p = q = 0

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}