Question

find the projection of the vectr i-j (cap) on the vector i+j (cap)?

Answer 1

Answer on Question #64469 – Math – Analytic Geometry

Question

Find the projection of the vector $i-j$ (cap) on the vector $i+j$ (cap).

Solution

Projection of resulting vector $\vec{i} - \vec{j}$ on resulting vector $\vec{i} + \vec{j}$ can be represented as

$$\frac{(\vec{i} - \vec{j}) \cdot (\vec{i} + \vec{j})}{|\vec{i} + \vec{j}|} = \frac{\vec{i}^2 - \vec{j}^2}{\sqrt{\vec{i}^2 + 2 \vec{i} \cdot \vec{j} + \vec{j}^2}} = \frac{1 - 1}{\sqrt{1 + 2 \cdot 1 \cdot 1 \cdot \cos \theta + 1}} = 0,$$

because vectors $\vec{i}$ and $\vec{j}$ are unit vectors, $\theta = 90{}^\circ$ is the angle between them.

Answer: 0.

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