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Motion in a Plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane3 Marks
Question
Prove that the vectors $\vec{\text{A}}=2\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{B}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ are mutuallly perpendicular.
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Answer

$\vec{\text{A}}.\vec{\text{B}}=(2\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}}).(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}})$ $\text{AB}\cos\theta=(2)(1)+(-3)(1)+(1)(1)=0$ $\text{AB}\cos\theta=0\ (\text{as A}\neq0,\text{ B}\neq0)$ $\therefore\ \theta=90^\circ$or, the vectors $\vec{\text{A}}$ and $\vec{\text{B}}$ are mutually perpendicular.

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