If vec{a}=(p, -2, 5) and vec{b}=(1, q, -3) ar | vedclass

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(D) Two vectors $\vec{a}$ and $\vec{b}$ are collinear if $\vec{a} = \lambda \vec{b}$ for some scalar $\lambda$. Given $\vec{a} = p\hat{i} - 2\hat{j} +

Vedclass · Accepted Answer

$p=\frac{-5}{3}, q=\frac{6}{5}$

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(D) Two vectors $\vec{a}$ and $\vec{b}$ are collinear if $\vec{a} = \lambda \vec{b}$ for some scalar $\lambda$. Given $\vec{a} = p\hat{i} - 2\hat{j} + 5\hat{k}$ and $\vec{b} = 1\hat{i} + q\hat{j} - 3\hat{k}$. Equating components: $p = \lambda(1) \implies p = \lambda$ $-2 = \lambda(q) \implies -2 = \lambda q$ $5 = \lambda(-3) \implies \lambda = -\frac{5}{3}$ Substituting $\lambda = -\frac{5}{3}$ into the other equations: $p = -\frac{5}{3}$ $-2 = (-\frac{5}{3})q \implies q = -2 	imes (-\frac{3}{5}) = \frac{6}{5}$ Thus,$p = -\frac{5}{3}$ and $q = \frac{6}{5}$.

If $\vec{a}=(p, -2, 5)$ and $\vec{b}=(1, q, -3)$ are collinear vectors,then:

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