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Consider the two vectors and . Calculate ' ' if both the vectors are perpendicular to each other…

Mathematics20254 marksShort answer
Consider the two vectors $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = 5\hat{i} + q\hat{j} - \hat{k}$.
(i)[1.0]
Calculate '$q$' if both the vectors are perpendicular to each other.
(ii)[2.0]
Find the unit vector perpendicular to both $\vec{a}$ and $\vec{b}$ if $q = 4$.
(iii)[1.0]
Find the projection of $\vec{a}$ on $\vec{b}$ if $q = 1$.

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Vectors

From ISC 2025 Improvement Mathematics Paper 1, question 17.