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Question

Let vectors a=6i3jk and b=2i+3j+k, find a unit vector which is perpendicular to the vectors a+b and ab.

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Solution

(a+b)=8i+0^j+0^k[ab,a.b=0](ab)=4i6^j2^kLetunitvectorni+yj+2^k(xi+yj+z^k).8i=8k=0(4i6^j2^k).(xi+yj+z^k)=04x6y2z=03y+z=0(i)x2+y2+z2=1y2+z2=1fromed(i),(3y)2=y2=1,10y2=1,y=±110Puty=±110inequation(i),z=±310Then,unitvectoris(0i+110y310^k)or(^j10+310^k)

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