Subjective Type

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

Solution

Let $$\vec {a}=2\hat {i}-3\hat {j}+4\hat {k}$$ and $$\vec {b}=-4\hat {i}+6\hat {j}-8\hat {k}$$

It is observed that $$\vec {b}=4\hat {i}+6\hat {j}-8\hat {k}=-2(2\hat {i}-3\hat {j}+4\hat {k})=-2\vec {a}$$

$$\therefore \vec {b}=\lambda \vec {a},$$ where $$\lambda =-2$$

Hence, the given vectors are collinear.

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