Show that the vectors 2 i -3 j +4 k and -4 i +6 j -8 k are collin… - Vidyadip

Question

Show that the vectors $2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and $-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$ are collinear.

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Answer

Given the position vectors $2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and $-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$Let $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$
Then,
$\vec{\text{b}}=-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$
$=-2\big(2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)$
$=-2\vec{\text{a}}$
Hence, $\vec{\text{a}},\vec{\text{b}}$ are collinear.

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