$\"\"$

Consider $\"\"$ and $\"\"$ are two non zero vectors.

(a)

Scalar projection of $\"\"$ onto $\"\"$ is $\"\"$ .

The condition $\"\"$ is possible when $\"\"$ .

$\"\"$ is when $\"\"$ .

The Scalar projection of $\"\"$ onto $\"\"$ is equal to the Scalar projection of $\"\"$ onto $\"\"$ is possible when the magnitude of $\"\"$ is equal to the magnitude of $\"\"$ or when $\"\"$ and $\"\"$ are orthogonal. $\"\"$

(b)

When $\"\"$ or if the two vectors are orthogonal then the condition $\"\"$ is possible.

If $\"\"$ and $\"\"$ are perpendicular and do not have the same length and the equation still holds then $\"\"$ is possible.

$\"\"$

(a) $\"\"$ is when $\"\"$ .

(b) $\"\"$ is possible when $\"\"$ .