Question

for two vectors a vector and b vector If a vector + b vector equal to C vector and a + b equals to C then prove that a vector and b vector are parallel to each other​

Answer 1

A vector + B vector = C vector
A + B = C

A vector + B vector (R^2)= A^2 + B^2 + 2ABcos theta
=>(C vector)^2= (A+B)^2 - 2AB + 2ABcos theta ...(i)
=>(C vector)^2= C^2 - 2AB( 1 - cos theta)
=>2AB( 1- cos theta) = 0
=> 1 - cos theta = 0
=>2 sin^2 theta/2 = 0 [ 1 - cos theta =2 sin^2 theta/2]
=> sin^2 theta/2 = 0
we know sin 0° = 0
thus, theta/2 = 0°
=> theta = 0

in eq(i), theta = 0
therefore the two vectors are parallel to each other...

hence, proved.

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