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Vectors & 3D Geometry

JEE Main level, numerical answer, medium

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Question 3 of 4

If $\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{b} = \hat{i} - 2\hat{j} + 4\hat{k}$ , the value of the dot product $\vec{a} \cdot \vec{b}$ is:

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Answer: -8

\vec{a} \cdot \vec{b} = (2)(1) + (3)(-2) + (-1)(4) = 2 - 6 - 4 = -8

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

Vectors & 3D GeometryIf 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:
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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 a⃗=2i^+3j^−k^\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}a=2i^+3j^​−k^ and b⃗=i^−2j^+4k^\vec{b} = \hat{i} - 2\hat{j} + 4\hat{k}b=i^−2j^​+4k^, the value of the dot product a⃗⋅b⃗\vec{a} \cdot \vec{b}a⋅b is:

JEE Main question paper PDF

More Mathematics practice

If $\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{b} = \hat{i} - 2\hat{j} + 4\hat{k}$ , the value of the dot product $\vec{a} \cdot \vec{b}$ is: