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

The cosine values of the angles made by the vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ with the $X$,$Y$,and $Z$ axes respectively are:

$A$ force,$\vec{F}=(4 \hat{i}+3 \hat{j}-5 \hat{k}) \text{ N}$,is acting on a body. If the horizontal direction is taken along the $\hat{i} + \hat{j}$ direction,find the angle $\theta$ that the force makes with this horizontal direction.

Write the distributive law for the product of two vectors.

Find $|\Delta \overrightarrow{a}|$ and $\Delta a$ when a vector $\overrightarrow{a}$ is rotated by an angle $d\theta$.

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