AP EAMCET · Maths · Vector Algebra
Let \(\mathbf{u}\) and \(\mathbf{v}\) be two vectors in \(R^2\). If \(|\mathbf{u}+\mathbf{v}|^2=2\left(|\mathbf{u}|^2+|\mathbf{v}|^2\right)\), then .....
- A \(\mathbf{u}=\mathbf{v}\)
- B \(\mathbf{u}\) and \(\mathbf{v}\) need not be same but they have same direction
- C \(\mathbf{u}\) and \(\mathbf{v}\) need not be same but they have the opposite direction
- D \(\mathbf{u}=2 \mathbf{v}\)
Answer & Solution
Correct Answer
(A) \(\mathbf{u}=\mathbf{v}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }|\mathbf{u}+\mathbf{v}|^2=2\left(|u|^2+|v|^2\right) \\ &|\mathbf{u}|^2+|\mathbf{v}|^2+2 \mathbf{u v}=2|\mathbf{u}|^2+2|\mathbf{v}|^2 \\ &|\mathbf{u}|^2+|\mathbf{v}|^2=2 \mathbf{u} \cdot \mathbf{v} \\ &|\mathbf{u}|^2+|\mathbf{v}|^2-2 \mathbf{u} \cdot…
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