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  4. Three vectors are given as P =3 hat i -4 hat j , Q =6 hat i -8 hat j and R =(3 / 4) hat i - hat j , then which of the following is correct?

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Q. Three vectors are given as $P =3 \hat{ i }-4 \hat{ j }, Q =6 \hat{ i }-8 \hat{ j }$ and $R =(3 / 4) \hat{ i }-\hat{ j }$, then which of the following is correct?

Motion in a Plane

Solution:

Given, $P =3 \hat{ i }-4 \hat{ j }$
and $ Q =6 \hat{ i }-8 \hat{ j }=2(3 \hat{ i }-4 \hat{ j })=2 P $
Also, $ R =\frac{3}{4} \hat{ i }-\hat{ j }=\frac{1}{4}(3 \hat{ i }-4 \hat{ j })=\frac{ P }{4}$
So, $P , Q$ and $R$ are parallel with unequal magnitude. Thus, they are not equals vectors.