Which of the following colours has the highest energy if the wavelengths of violet, blue, yellow, and red light are $410 \text{ nm}$, $470 \text{ nm}$, $580 \text{ nm}$, and $750 \text{ nm}$ respectively?

$A$ 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.

In a regular octagon $ABCDEFGH$ with center $O$,what is the sum of $\overrightarrow{ AB }+\overrightarrow{ AC }+\overrightarrow{ AD }+\overrightarrow{ AE }+\overrightarrow{ AF }+\overrightarrow{ AG }+\overrightarrow{ AH }$ if $\overrightarrow{ AO }=2 \hat{ i }+3 \hat{ j }-4 \hat{ k }$?

$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. Find $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} = \ldots \ldots$.

The component of a vector $\vec{A}$ along a direction making an angle $\theta$ with it is given by $A \cos \theta$. What can be said about the magnitude of this component?

$A$ vector $\vec{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively. Then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $