Source: Extra Practice

The projection of vector A⃗=i^+j^\vec{A} = \hat{i} + \hat{j} on the vector B⃗=i^−j^\vec{B} = \hat{i} - \hat{j} is:

Options

Option A is correct

00

Option B

22

Option C

2\sqrt{2}

Option D

1/21/\sqrt{2}

Explanation

The projection of vector A⃗\vec{A} on B⃗\vec{B} is given by the formula projB⃗A⃗=A⃗⋅B⃗∣B⃗∣\text{proj}_{\vec{B}}\vec{A} = \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}. Calculating the dot product: A⃗⋅B⃗=(1)(1)+(1)(−1)=1−1=0\vec{A} \cdot \vec{B} = (1)(1) + (1)(-1) = 1 - 1 = 0. Since the dot product is zero (the vectors are perpendicular), the projection is 0∣B⃗∣=0\frac{0}{|\vec{B}|} = 0. Hence, option 1 is correct, and the other options are mathematically incorrect.