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MHT CET 2025 (22 Apr, Shift 2) · Scalar (Dot) Product

Scalar (Dot) Product question from MHT CET 2025 (22 Apr, Shift 2)

Q10MHT CET 2025 · 22 APR · SHIFT 2Easy

Scalar (Dot) Product

Given A⃗=(2i^−3j^+k^),B⃗=(3i^+j^−2k^)\vec{A} = (2\hat{i} - 3\hat{j} + \hat{k}), \quad \vec{B} = (3\hat{i} + \hat{j} - 2\hat{k}) and C⃗=(3i^+2j^+k^)\vec{C} = (3\hat{i} + 2\hat{j} + \hat{k}), then (A⃗+B⃗)⋅C⃗(\vec{A} + \vec{B}) \cdot \vec{C} will be

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Answer: (a)

  1. A⃗+B⃗=5i^−2j^−k^\vec{A} + \vec{B} = 5\hat{i} - 2\hat{j} - \hat{k}
  2. (A⃗+B⃗)⋅C⃗=5(3)+(−2)(2)+(−1)(1)=15−4−1=10(\vec{A} + \vec{B}) \cdot \vec{C} = 5(3) + (-2)(2) + (-1)(1) = 15 - 4 - 1 = 10
  3. So the answer is (a) 10.
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