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Find the corrdinates of the point which ...

Find the corrdinates of the point which divides the line segment joining the points A(2,-6,8) and B (-1,3,-4) externally in the ratio 1:3.

Text Solution

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Let `bar(a)` and `bar(b)` be position vectors of A and B respectively.
Then `bar(a)=2hat(i)-6hat(j)+8hat(k)` and `bar(b)=-hat(i)+3hat(j)-4hat(k)`.
Let `C(bar(c))` divides AB externally in the ratio 1:3.
`:.bar(c)=(1*bar(b)-3*bar(a))/(1-3)=((-hat(i)+3hat(j)-4hat(k))-3(2hat(i)-6hat(j)+8hat(k)))/(-2)`
`=-(1)/(2)(-hat(i)+3hat(j)-4hat(k)-6hat(i)+18hat(j)-24hat(k))`
`=-(1)/(2)(-7hat(i)+21hat(j)-28hat(k))`
`:.bar(c)=(7)/(2)hat(i)-(21)/(2)hat(j)+14hat(k)" ":.` coordinates of C are `((7)/(2),-(21)/(2),14)`.
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