Question

The projection of $\overrightarrow{A}$ on $\overrightarrow{B}$ is
A. $\overrightarrow{A}\bullet \overrightarrow{B}$
B. $\overrightarrow{A}\bullet \widehat{B}$
C. $\overrightarrow{B}\bullet \overrightarrow{A}$
D. $\widehat{A}\bullet \widehat{B}$

Answer 1

As a first step, you could read the question along with the options to understand the exact thing to be found. Then, you could simply give a brief description on the projection of one vector onto another. You could also give how they are categorized. After that one could give how this is mathematically expressed.

Complete step-by-step solution:
In the question we are given two vectors, namely, vector A and vector B. We are supposed to find the projection of $\overrightarrow{A}$ on the other vector$\overrightarrow{B}$.
On projecting one vector onto another gives the answer the following question explicitly. Doing so tells us how much of one vector goes in the direction of the other vector.
Basically, when we say vector projection of A on B, it simply means that the new vector is going along B. When we resolve a vector we get a component that is parallel to the other vector and one that is perpendicular to it. So the vector projection if one vector on another is the vector component that is parallel.
Now, we have the scalar projection which is defined as the length of this vector projection. Also, the scalar projection is normally given by the dot product of one vector with the unit vector for that particular direction.
So, the projection of $\overrightarrow{A}$ on $\overrightarrow{B}$ would be given by $\overrightarrow{A}\bullet \widehat{B}$
Hence, option B is the correct answer.

Note: Since we weren’t specified on whether to find the vector projection or scalar projection we have found the scalar projection as we normally mean the scalar projection by ‘projection’. Also, the vector projection vector A on vector B is given by,
$\left( \dfrac{A\bullet B}{\left| B \right|} \right)\dfrac{B}{\left| B \right|}$