If a unit vector is represented as $\overrightarrow{u} = 0.4 \hat{i} + 0.7 \hat{j} + c \hat{k}$,then the value of '$c$' is

Write the distributive law for the product of two vectors.

$A$ 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.

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 $^{\circ}$)

There are two vectors $\vec{A} = 6\hat{i} + 9\hat{j} - \hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k}$ which have the same direction. The value of '$p$' is

The unit vector $\hat{n} = (a \hat{\imath} + b \hat{\jmath})$ is perpendicular to the vector $\vec{r} = (\hat{\imath} + \hat{\jmath})$. Which of the following is a possible value for $b$?