The two vectors A→$$=-2i^+3j^+yk^$$ and B→$$=i^+2j^+xk^$$ are perpendicular. Given $$x+y=0$$. Find x and y?

Correct option is 2x=2 and y=-2

Questions

The two vectors $\vec{A} = - 2 \hat{i} + 3 \hat{j} + y \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} + x \hat{k}$ are perpendicular. Given $x + y = 0$ . Find x and y?

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x=2 and y=-1

x=2 and y=-2

x=1 and y=-2

x=1 and y=-1

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detailed solution

Correct option is B

x+y=0when the vectors are perpendicular.A→.B→=AxBx+AyBy+AzBz =0A→.B→=-2+6+xy=0⇒xy=-4x-y2=x+y2-4xyx-y=±4x=2 and y=-2 or x=-2 and y=2

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The two vectors A→=-2i^+3j^+yk^ and B→=i^+2j^+xk^ are perpendicular. Given x+y=0. Find x and y?

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The two vectors $\vec{A} = - 2 \hat{i} + 3 \hat{j} + y \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} + x \hat{k}$ are perpendicular. Given $x + y = 0$ . Find x and y?