If a⃗ = î + 2ĵ + 3k̂ and b⃗ = -î + 2ĵ + k̂ and c⃗ = 3î + ĵ, find t such that a⃗ + tb⃗ is perpendicular to c⃗ is

Answer: (b) 5 a⃗ + tb⃗ = (1 - t)î + (2 + 2t)ĵ + (3 + t)k̂. Perpendicular to c⃗: 3(1 - t) + (2 + 2t) = 0 ⇒ 5 - t = 0, so t = 5. Correct: (b)

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If a⃗ = î + 2ĵ + 3k̂ and b⃗ = -î + 2ĵ + k̂ and c⃗ = 3î + ĵ, find t such that a⃗ + tb⃗ is…

If $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j}$, find $t$ such that $\vec{a} + t\vec{b}$ is perpendicular to $\vec{c}$ is

(a)$0$
(b)$5$
(c)$4$
(d)$2$

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Answer

Correct option: (b)

Answer: (b) $5$ $\vec{a} + t\vec{b} = (1 - t)\hat{i} + (2 + 2t)\hat{j} + (3 + t)\hat{k}$. Perpendicular to $\vec{c}$: $3(1 - t) + (2 + 2t) = 0 \Rightarrow 5 - t = 0$, so $t = 5$.