Grade 9Mechanics
If a vector+ b vector=c vector and a^2+=b^2+c^2,then prove that a and b are perpendicular to eCh other
If a vector+ b vector=c vector and a^2+=b^2+c^2,then prove that a and b are perpendicular to eCh other
1 Answer
AKSHANSH PAREEK
Given A+B=C and A^2+B^2=C^2.
(A+B).(A+B)=C.C
=>A.A+A.B+B.A+B.B=C.C
=>A^2+2A.B+B^2=C^2
=>2A.B=0
=>A.B=0
=>|A||B|cosθ=0
=>cosθ=0
=>θ=π/2
(A+B).(A+B)=C.C
=>A.A+A.B+B.A+B.B=C.C
=>A^2+2A.B+B^2=C^2
=>2A.B=0
=>A.B=0
=>|A||B|cosθ=0
=>cosθ=0
=>θ=π/2
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