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Solve the following.
Consider the two vectors and . Calculate ' ' if both the vectors are perpendicular to each other.
Consider the two vectors $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = 5\hat{i} + q\hat{j} - \hat{k}$.
Calculate '$q$' if both the vectors are perpendicular to each other.
Answer
Answer
AIThe vectors are perpendicular, so $\vec{a}\cdot\vec{b} = 0$: $2(5) + (-3)(q) + 4(-1) = 0$, so $10 - 3q - 4 = 0$ and $q = 2$.
Final answer: $2$
From ISC 2025 Improvement Mathematics Paper 1, question 17(i).
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