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JEE • MATHEMATICS • SCALAR TRIPLE PRODUCT

Scalar triple product practice · Medium

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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31 Medium

31 of 38

Application +4 | -1

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

are vectors such that

[\vec{a} \vec{b} \vec{c}]=4

then

[\vec{a} \times \vec{b} \vec{b} \times \vec{c} \vec{c} \times \vec{a}]=

View answer and explanation

Correct option: A

Option A (16) is correct because the scalar triple product of cross products simplifies to the square of the original scalar triple product.

32 Medium

32 of 38

Understanding +4 | -1

If a, b and

\mathbf{c}

be any three non-zero and non-coplanar vectors, then any vector

r

is equal to
where,

x=\frac{[\mathbf{r} \mathbf{b} \mathbf{c}]}{[\mathbf{a} \mathbf{b} \mathbf{c}]}, y=\frac{[\mathbf{r} \mathbf{c} \mathbf{a}]}{[\mathbf{a} \mathbf{b} \mathbf{c}]^{,}} z=\frac{[\mathbf{r} \mathbf{a} \mathbf{b}]}{[\mathbf{a} \mathbf{b} \mathbf{c}]}

View answer and explanation

Correct option: B

x a+y b+x

Option D (None of these) is incorrect, the correct answer should be

\mathbf{r} = x\mathbf{a} + y\mathbf{b} + z\mathbf{c}

, but it is not listed in the given options. The correct answer is a linear combination of the vectors a, b, and c.

33 Medium

33 of 38

Application +4 | -1

The distance between the lines

\bar{r}=(\bar{i}+2 \bar{j}-4 \bar{k})+\lambda(2 \bar{i}+3 \bar{j}+6 \bar{k})

\bar{r}=(3 \bar{i}+3 \bar{j}-5 \bar{k})+\mu(2 \bar{i}+3 \bar{j}+6 \bar{k})

View answer and explanation

Correct option: C

\frac{\sqrt{293}}{7}

Option B (

\frac{{\sqrt{{293}}}}{{7}}

) is correct because it represents the distance between the two lines, calculated using the formula for the distance between parallel lines in vector form.

34 Medium

34 of 38

Application +4 | -1

Given vectors

\mathbf{a}, \mathbf{b}, \mathbf{c}

such that

\mathbf{a}(\mathbf{b} \times \mathbf{c})=\lambda \neq 0

, the value of

(\mathbf{b} \times \mathbf{c}) .(\mathbf{a}+\mathbf{b}+\mathbf{c}) / \lambda

View answer and explanation

Correct option: C

-3 \lambda

Option B (1) is correct because

(\mathbf{b} \times \mathbf{c}) .(\mathbf{a}+\mathbf{b}+\mathbf{c}) / \lambda

simplifies to

\lambda / \lambda = 1

since

(\mathbf{b} \times \mathbf{c}) . \mathbf{b}

and

(\mathbf{b} \times \mathbf{c}) . \mathbf{c}

are zero.

35 Medium

35 of 38

Application +4 | -1

The line

I_1

passes through the point

(2,6,2)

and is perpendicular to the plane

2 x+y-2 z=10

. Then the shortest distance between the line

h

and the line

\frac{x+1}{2}=\frac{y+4}{-3}=\frac{z}{2}

View answer and explanation

Correct option: C

Option C (9) is correct because it represents the shortest distance between the two lines, calculated using the formula for skew lines.

36 Medium

36 of 38

Application +4 | -1

\mathbf{a}=(1,-1,1)

and

\mathbf{c}=(-1,-1,0)

, then the vector

\mathbf{b}

satisfying

\mathbf{a} \times \mathbf{b}=\mathbf{c}

and

\mathbf{a} \cdot \mathbf{b}=1

View answer and explanation

Correct option: B

(0,0,1)

Option B ((0,0,1)) is correct because it satisfies both the cross product and dot product conditions with the given vectors a and c.

37 Medium

37 of 38

Application +4 | -1

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

are unit coplanar vectors, then

\left[ {2\mathbf{\vec a} - \mathbf{\vec b}\;2\;\mathbf{\vec b} - \mathbf{\vec c}\;2\;\mathbf{\vec c} - \mathbf{\vec a}} \right]

is equal to

View answer and explanation

Correct option: B

Option B (0) is correct because if three vectors are coplanar, any linear combination of them will also be coplanar, resulting in a scalar triple product of zero.

38 Medium

38 of 38

Application +4 | -1

\vec{d}=\lambda(\vec{a} \times \vec{b})+\mu(\vec{b} \times \vec{c})+\gamma(\vec{c} \times \vec{a})

and

[\vec{a}, \vec{b}, \vec{c}]=1

Then

\lambda+\mu+\gamma

is equal to

View answer and explanation

Correct option: A

\vec{d} \cdot(\vec{a}+\vec{b}+\vec{c})

Option A (\vec{d} ·(\vec{a}+\vec{b}+\vec{c})) is correct because it simplifies to λ + μ + γ using the scalar triple product property and the given condition.

Revision notes and key takeaways

Review SCALAR TRIPLE PRODUCT in your textbook or class notes, then use this set to check your understanding.

Showing 31-38 of 38 questions

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