A unit vector coplanar with $\widehat {\bf{i}} + \widehat {\bf{j}} + 2{\bf{\hat k}}$ and $\widehat {\bf{i}} + 2\widehat {\bf{j}} + {\bf{\hat k}}$, and perpendicular to $\widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}}$ is

$\left( {\frac{{\widehat {\bf{j}} - {\bf{\hat k}}}}{{\sqrt 2 }}} \right)$

$\left( {\frac{{\widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}}}}{{\sqrt 3 }}} \right)$

$\left( {\frac{{\widehat {\bf{i}} + \widehat {\bf{j}} + 2{\bf{\hat k}}}}{{\sqrt 6 }}} \right)$

$\left( {\frac{{\widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}}}}{{\sqrt 6 }}} \right)$

Back to SCALAR TRIPLE PRODUCT

Your Progress

0 / 3 Answered

Correct

Incorrect

Accuracy

JEE • MATHEMATICS • SCALAR TRIPLE PRODUCT

Scalar triple product practice · Hard

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

Practice format and chapter quiz

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.

Take a chapter quiz →

1 Hard

1 of 3

Application +4 | -1

Let

\vec a = \hat i - 2\hat j + 3\hat k,\;\vec b = 3\hat i + 3\hat j - \hat k

and

\vec c = d\hat i + \hat j + \left( {2d - 1} \right)\hat k

. If

{\vec c}

is parallel to the plane of the vectors

{\vec a}

and

{\vec b}

, then

11d =

View answer and explanation

Correct option: C

- 1

Option C (-1) is correct because the condition for a vector to be parallel to the plane of two other vectors is correctly applied using the scalar triple product.

2 Hard

2 of 3

Application +4 | -1

A vector

\mathbf{n}

of magnitude 8 units is inclined to

x

-axis at

45^{\circ}, y

-axis at

60^{\circ}

and an acute angle with

z

-axis. If a plane passes through a point

(\sqrt{2},-1,1)

and is normal to

\mathbf{n}

, then its equation in vector form is

View answer and explanation

Correct option: B

\mathbf{r} \cdot(\sqrt{2} \mathbf{i}+\mathbf{j}+\mathbf{k})=2

Option B (

\mathbf{r} \cdot(\sqrt{2} \mathbf{i}+\mathbf{j}+\mathbf{k})=2

) is correct because it is the equation of the plane passing through the given point and normal to the vector

\mathbf{n}

3 Hard

3 of 3

Application +4 | -1

A unit vector coplanar with

\widehat \mathbf{i} + \widehat \mathbf{j} + 2\mathbf{\hat k}

and

\widehat \mathbf{i} + 2\widehat \mathbf{j} + \mathbf{\hat k}

, and perpendicular to

\widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k}

View answer and explanation

Correct option: A

\left( {\frac{{\widehat \mathbf{j} - \mathbf{\hat k}}}{{\sqrt 2 }}} \right)

Option A (

\left( {\frac{{\widehat \mathbf{j} - \mathbf{\hat k}}}{{\sqrt 2 }}} \right)

) is correct because it is a unit vector that is coplanar with the given vectors and perpendicular to

\widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k}

Revision notes and key takeaways

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

Key Takeaways

✓ This set contains 3 single-correct-answer MCQs on SCALAR TRIPLE PRODUCT.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

Continue Your Practice

📚 Switch Set (HARD)

Chapter Sets

ALL 230 MCQs EASY 189 MCQs HARD 3 MCQs MEDIUM 38 MCQs

0 /3

0✓ 0✗

0% Accuracy