Question

for two vectors A and B If A vector + B vector =C vector and A+B= C ,then prove that A vector and B vector are parallel to each other

Answer 1

for two vectors A and B .

$\vec{A}+\vec{B}=\vec{C}$

or, $\bf{|A+B|=|C|}$

or, $\bf{\sqrt{A^2+B^2+2ABcos\theta}=C}$

or, $\bf{A^2+B^2+2ABcos\theta=C^2}$

given, A + B = C

so, C² = (A + B)² using it in above expression.

or, $\bf{A^2+B^2+2ABcos\theta=(A+B)^2}$

or, $A^2+B^2+2ABcos\theta=A^2+B^2+2AB$

or, $2ABcos\theta=2AB$

or, $cos\theta=1=cos0^{\circ}$

and angle between A and B is zero. means, vector A and vector B are parallel to each other .

Answer 2

Answer:

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