What is the projection of vector i + j on vector i - j?

B. 0 — The projection of vector a on vector b is given by the dot product of a and b divided by the magnitude of b. Since the dot product of i + j and i - j is 1 minus 1 which equals 0, the projection is 0.

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$What is the projection of vector a = \hat{i} + \hat{j} on vector b = \hat{i} - \hat{j} ?$

A. $1$
B. $0$
C. $- 1$
D. $2$

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Correct answer: B — $0$

Solution

The projection is given by \frac{a \cdot b}{∣ b ∣} . Here, a \cdot b = (1) (1) + (1) (- 1) = 1 - 1 = 0 . Thus, the projection is 0 .

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What is the projection of vector a=i^+j^​ on vector b=i^−j^​?

Solution

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$What is the projection of vector a = \hat{i} + \hat{j} on vector b = \hat{i} - \hat{j} ?$