If and are two vectors in and system

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If z1=ai^+bj^\mathbf{z}_1 = a\hat{i} + b\hat{j} and z2=ci^+dj^\mathbf{z}_2 = c\hat{i} + d\hat{j} are two vectors in i^\hat{i} and j^\hat{j} system, where ∣z1∣=∣z2∣=r|\mathbf{z}_1| = |\mathbf{z}_2| = r and z1⋅z2=0\mathbf{z}_1 \cdot \mathbf{z}_2 = 0 , then w1=ai^+cj^\mathbf{w}_1 = a\hat{i} + c\hat{j} and w2=bi^+dj^\mathbf{w}_2 = b\hat{i} + d\hat{j} satisfy (1) ∣w1∣=r|\mathbf{w}_1| = r (2) ∣w2∣=r|\mathbf{w}_2| = r (3) w1⋅w2=0\mathbf{w}_1 \cdot \mathbf{w}_2 = 0 (4) None of the above

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