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Question

If the three successive vertices of a parallelogram have the position vectors as, A(3,2,0);B(3,3,1) and C(5,0,2). Then find :
a vector having the same direction as that of AB but magnitude equal to AC

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Solution

A(3,2,0) B(3,3,1) C(5,0,2)
OA=3^i2^j0 OB=3^i3^j+^k OC=5^i+2^k

AC=OCOA=5^i+2^k(3^i2^j)

AC=8^i+2^j+2^k

|AC|=82+72+22=72

AB=OBOA=(3^i3^j^k)(3^i^j)

AB=6^i^j+^k

Vector in direction of AB=k(6^i^j+^k)

it has magnitude 72

72=(6k)2+(k)2+k2

72=k38

k=7238=3619=619

Vector direction of vecAB which magnitude of AC

619(6^i^j+^k)


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