Let $\vec{a}, \vec{b}, \vec{c}$ be three unit vectors such that $\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0.$ If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3},$ then the volume of the parallelopiped whose three coterminous edges are $\vec{a}, \vec{b}, \vec{c}$ is

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

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Application +4 | -1

Let

\vec{a}, \vec{b}, \vec{c}

be three unit vectors such that

\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0.

If the angle between

\vec{b}

and

\vec{c}

\frac{\pi}{3},

then the volume of the parallelopiped whose three coterminous edges are

\vec{a}, \vec{b}, \vec{c}

View answer and explanation

Correct option: A

\frac{\sqrt{3}}{2}

cubic units

Option A (

\frac{\sqrt{3}}{2}

cubic units) is correct because the volume of the parallelepiped is calculated using the scalar triple product, considering the given dot product and unit vector conditions.

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

for some non-zero vector

\vec r,

then the value of

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

is The shortest distance between the lines

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

and

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

is Let

\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}

and

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

Then

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

depends on If

\vec{a}, \vec{b}

are non-zero vectors, then

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

equals

a \cdot(a \times b)=

The length of the perpendicular from the origin to the plane passing through the point a and containing the line

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