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Question

Magnitudes of vectors a,b,c are 3,4,5 respectively. If a and b+c, b and c+a, c and a+b are mutually perpendicular, then the magnitude of a+b+c is,

A
42
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B
32
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C
52
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D
33
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Solution

The correct option is C 52
a(b+c)=0ab+ac=0

Similarly, bc+ba=0

ca+cb=0

Adding these 2(ab+bc+ca)=0

Now |a+b+c|2=|a|2+|b|2+|c|2+2(ab+bc+ca)

=9+16+25=50

|a+b+c|=52

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