Question
Show that vectors $\text{A}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}$ and $\text{B}=-6\hat{\text{i}}+9\hat{\text{j}}+3\hat{\text{k}}$
are parallel.
are parallel.
✓
Answer
The given vectors are $\text{A}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}$ and $\text{B}=-6\hat{\text{i}}+9\hat{\text{j}}+3\hat{\text{k}}$ Then, the vecotrs are parallel, if A × B = 0 $\therefore\ \text{A}\times\text{B}=\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}}\\2&-3&-1\\-6&9&3\end{vmatrix}$ $\hat{\text{i}}(-9+9)-\hat{\text{j}}(6-6)+\hat{\text{k}}(18-18)=0$ But |A × B| = 0 $\text{AB}\sin\theta=0\ \ [\because\text{A}\neq0\text{ and B}\neq0]$ $\therefore\ \sin\theta=0\ \text{or }\theta=0$ Hence, the vectors A and B are parallel.
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