Given $A = 3\hat{i} + 4\hat{j}$ and $B = 7\hat{i} + 24\hat{j}$,find a vector that has the same magnitude as $B$ and is parallel to $A$.

The five sides of a regular pentagon are represented by vectors $A_1, A_2, A_3, A_4$ and $A_5$ in cyclic order as shown in the figure. Corresponding vertices are represented by vectors $B_1, B_2, B_3, B_4$ and $B_5$,drawn from the center of the pentagon. Then,$B_2 + B_3 + B_4 + B_5$ is equal to:

Match Column $-I$ with Column $-II$.

Column $-I$	Column $-II$
$(1)$ Angular momentum	$(a)$ Scalar
$(2)$ Potential energy	$(b)$ Vector
	$(c)$ Unit vector

Find the magnitude and direction of the vector $\vec{A} = \hat{i} + \hat{j}$.

If a vector $\overrightarrow{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C = 0$. Out of three vectors,two are equal in magnitude and the magnitude of the third vector is $\sqrt{2}$ times that of either of the two having equal magnitude. Then the angles between the vectors are given by: