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Question

The directions cosines of the joins of the following pairs of vectors :
(i) (6,3,2),(5,1,4) be k3,m3,m3
(ii) (3,4,7),(0,2,5) be n7,l7,m7
Find k+m+n+l ?

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Solution

For P(x1y1z1) and Q(x2y2z2)

Direction cosines are x2x1PQ,y2y1PQ,z2z1PQ

Now for P(6,3,2),Q(5,1,4)

PQ=(65)2+(31)2+(24)2=1+4+4=3

And direction cosine 653,313,243=13,23,23

And for A(3,4,7),B(0,2,5)

AB=(30)2+(42)2+(72)2=9+36+4=49=7

Direction cosine is 307,427,757=37,67,27

k+m+n+l=1+2+36=0


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