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Find a vector which is perpendicular to both A and B but has a magnitude equal to that of B A=3i^-2j^,b=4i^+3j^-k^

Asked by Sunita | 01 Jun, 2019, 23:27: PM

Expert Answer

Let's say

C with rightwards harpoon with barb upwards on top

be the vector perpendicular to both

A with rightwards harpoon with barb upwards on top space a n d space B with rightwards arrow on top

and

C with rightwards arrow on top equals A with rightwards harpoon with barb upwards on top cross times B with rightwards harpoon with barb upwards on top equals open vertical bar table row i j k row 3 cell negative 2 end cell 0 row 4 3 cell negative 1 end cell end table close vertical bar equals 2 i plus 3 j plus 17 k U n i t space v e c t o r space C with hat on top equals fraction numerator C with rightwards harpoon with barb upwards on top over denominator open vertical bar C with rightwards harpoon with barb upwards on top close vertical bar end fraction equals fraction numerator 2 i plus 3 j plus 17 k over denominator square root of 302 end fraction T h e space n e w space v e c t o r space h a s space m a g n i t u d e space e q u a l space t o t h e space m a g n i t u d e space o f space bold B with bold rightwards harpoon with barb upwards on top equals square root of 4 squared plus 3 squared plus 1 end root equals square root of 26 T h e r e f o r e space t h e space v e c t o r space w h i c h space i s space p e r p e n d i c u l a r space t o space b o t h space v e c t o r A space a n d space B space a n d space h a s space m a g n i t u d e space e q u a l space t o space B space i s fraction numerator square root of 26 open parentheses 2 i plus 3 j plus 17 k close parentheses over denominator square root of 302 end fraction

Answered by Utkarsh Lokhande | 02 Jun, 2019, 12:01: PM

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