Find the projection of the vector a = 2i + 3j + 2k on the vector b = i + 2j + k . - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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Find the projection of the vector a = 2 \hat{i} + 3 \hat{j} + 2 \hat{k} on the vector b = \hat{i} + 2 \hat{j} + \hat{k} .

Solution & Step-by-step Explanation

Projection of a on b is given by \frac{a \cdot b}{∣ b ∣} .Calculate a \cdot b : a \cdot b = (2) (1) + (3) (2) + (2) (1) = 2 + 6 + 2 = 10 Calculate ∣ b ∣ : ∣ b ∣ = 1^{2} + 2^{2} + 1^{2} = 6 Calculate Projection: Projection = \frac{10}{6} = \frac{10 6}{6} = \frac{5 6}{3}

Try it yourself before checking the explanation above.

Find the projection of the vector a = 2 \hat{i} + 3 \hat{j} + 2 \hat{k} on the vector b = \hat{i} + 2 \hat{j} + \hat{k} .

\frac{2 6}{3}

\frac{4 6}{3}

\frac{5 6}{3}

None of these

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