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8.6.3 Vector Short Questions (Question 6 & 7)


Question 6:
The points P, Q and R are collinear. It is given that   PQ=4a˜2b˜  and   QR=3a˜+(1+k)b˜ , where k is a constant. Find
(a)    the value of k,
(b)    the ratio of PQ : QR.

Solution:
(a)
Note: If P, Q and R are collinear,PQ=mQR4a˜2b˜=m[3a˜+(1+k)b˜]4a˜2b˜=3ma˜+m(1+k)b˜Comparing vector:a˜: 4=3m        m=43b˜: 2=m(1+k)2=43(1+k)1+k=64k=321k=52

(b)
PQ=mQRPQ=43QRPQQR=43PQ:QR=4:3



Question 7:
Given that x˜=3i˜+mj˜ and   y˜=4i˜3j˜ , find the values of m if the vector   x˜  is parallel to the vector y˜ .

Solution:
If vector x˜ is parallel to vector y˜x˜=hy˜(3i˜+mj˜)=h(4i˜3j˜)3i˜+mj˜=4hi˜3hj˜Comparing vector:i˜:  3=4h        h=34j˜:  m=3h        m=3(34)=94

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