The projection of hat{i}-hat{j} on hat{i}+hat | vedclass

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Question

(C) The projection of a vector $\vec{a}$ on a vector $\vec{b}$ is given by the formula: $	ext{Projection} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) The projection of a vector $\vec{a}$ on a vector $\vec{b}$ is given by the formula: $	ext{Projection} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.Let $\vec{a} = \hat{i}-\hat{j}$ and $\vec{b} = \hat{i}+\hat{j}$.First,calculate the dot product $\vec{a} \cdot \vec{b} = (1)(1) + (-1)(1) = 1 - 1 = 0$.Since the dot product is $0$,the projection of $\vec{a}$ on $\vec{b}$ is $\frac{0}{|\vec{b}|} = 0$.Therefore,the correct option is $C$.

The projection of $\hat{i}-\hat{j}$ on $\hat{i}+\hat{j}$ is . . . . . . .

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