JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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The volume of the tetrahedron whose vertices are the points with position vectors

\mathbf{i}-6 \mathbf{j}+10 \mathbf{k},-\mathbf{i}-

3 \mathbf{j}+7 \mathbf{k}, 5 \mathbf{i}-\mathbf{j}+\lambda \mathbf{k}

and

7 \mathbf{i}-4 \mathbf{j}+7 \mathbf{k}

is 11 cubic units if the value of

\lambda

View answer and explanation

Correct option: B

Option D (5) is the correct answer because it results in a volume of 11 cubic units for the tetrahedron.

More Questions from SCALAR TRIPLE PRODUCT

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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}