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Consider the position vectors of , and as , and Calculate and . Find the projection of on . Find…
Consider the position vectors of $A$, $B$ and $C$ as $\vec{OA} = 2\hat{i} - 2\hat{j} + \hat{k}$, $\vec{OB} = \hat{i} + 2\hat{j} - 2\hat{k}$ and $\vec{OC} = 2\hat{i} - \hat{j} + 4\hat{k}$
(i)[1.0]
Calculate $\vec{AB}$ and $\vec{BC}$.
(ii)[1.0]
Find the projection of $\vec{AB}$ on $\vec{BC}$.
(iii)[2.0]
Find the area of the triangle $ABC$ whose sides are $\vec{AB}$ and $\vec{BC}$.
Answer
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From ISC 2025 Mathematics Paper 1, question 17.