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Question

If A=2^i3^j and B=4^i+2^j, then |A.B|= ___


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Solution

A=2^i3^jB=4^i+2^j,AB=(2^i3^j).(4^i+2^j)

=(2×4)(^i^i)+(2×2)(^i^j)+(3×4)(^j^i)(3×2)(^j^j)

Now ^i^i=^j^j=1(|^i||^i| cos 0=1)

^i^j=^j^i=0 (^i and ^j are perpendicular to each other)

So (2^i3^j).(4^i+2^j)

= -8 + 0 + 0 – 6

= -14

|A.B|=|14|=14


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