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Vectors & 3D Geometry

JEE Main level, single correct, medium

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Question 1 of 4

If vectors $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ , $\vec{b} = \hat{i} - \hat{j} + 2\hat{k}$ and $\vec{c} = x\hat{i} + \hat{j} - \hat{k}$ are coplanar, then $x$ is equal to:

Show answer and solution

Answer: (D) $-\frac{1}{3}$

Coplanar

\iff [\vec a\,\vec b\,\vec c] = 0

\begin{vmatrix} 1 & 1 & 1 \\ 1 & -1 & 2 \\ x & 1 & -1 \end{vmatrix} = 1(1-2) - 1(-1-2x) + 1(1+x) = 3x + 1 = 0 \implies x = -\frac{1}{3}

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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More Mathematics practice

JEE Main Mathematics practice question on Vectors & 3D Geometry, with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.

If vectors a⃗=i^+j^+k^\vec{a} = \hat{i} + \hat{j} + \hat{k}a=i^+j^​+k^, b⃗=i^−j^+2k^\vec{b} = \hat{i} - \hat{j} + 2\hat{k}b=i^−j^​+2k^ and c⃗=xi^+j^−k^\vec{c} = x\hat{i} + \hat{j} - \hat{k}c=xi^+j^​−k^ are coplanar, then xxx is equal to:

JEE Main question paper PDF

More Mathematics practice

If vectors $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ , $\vec{b} = \hat{i} - \hat{j} + 2\hat{k}$ and $\vec{c} = x\hat{i} + \hat{j} - \hat{k}$ are coplanar, then $x$ is equal to: