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Vectors A and B have the same nonzero magnitude (A = B), where

C = A + B and D=A-B

vectors.if the magnitude of C and D are the same , how are the directions of A and B related. Hint , sketch these vectors.

The angle between À and B is: - Select

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Given\begin{aligned}A & =B \\\& \vec{C} & =\vec{A}+\vec{B}-\text { (1) } \\f \vec{D} & =\vec{A}-\vec{B}-\text { (2) } \\C & =D\end{aligned}squaring eqn (1) f(2)\begin{array}{l}|\vec{C}|^{2}=C^{2}=(\vec{A}+\vec{B})^{2} \\\rho|\vec{D}|^{2}=D^{2}=(\vec{A}-\vec{B})^{2}\end{array}So\begin{array}{l}(\vec{A}+\vec{B})^{2}=(\vec{A}-\vec{B})^{2} \\A^{2}+B^{2}+ 2 A B \cos \theta=A^{2}+B^{2}-2 A B \cos \theta \\4 A B \cos \theta=0 \\\cos \theta=0 \\\theta=90^{\circ}\end{array} ...