The projection of vector $\vec{A}$ on $\vec{B}$ is:

The resultant of $\vec{A}$ and $\vec{B}$ makes an angle $\alpha$ with $\vec{A}$ and $\beta$ with $\vec{B}$. Which of the following is correct?

If $\vec{A} + \vec{B} = \vec{C}$ and $|\vec{A}| + |\vec{B}| = |\vec{C}|$,what can be said about the direction of these vectors?

Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is (in $^{\circ}$)

If $\overrightarrow A = 2\hat i + 4\hat j - 5\hat k$,the direction cosines of the vector $\overrightarrow A$ are:

$A$ vector has a magnitude the same as that of $\overrightarrow{A} = 3 \hat{i} + 4 \hat{j}$ and is parallel to $\overrightarrow{B} = 4 \hat{i} + 3 \hat{j}$. The $x$ and $y$ components of this vector in the first quadrant are $X$ and $3$ respectively,where $X = $ . . . . . . .