If $a^2 + b^2 + c^2 = 1$,then the maximum possible value of $3a + 4b + 12c$ is equal to (where $a, b, c \in \mathbb{R}$)-

For any two vectors $\vec{a}$ and $\vec{b}$,we always have $|\vec{a} \cdot \vec{b}| \leq |\vec{a}| |\vec{b}|$ (Cauchy-Schwarz inequality). Is this statement true or false?

If $\vec{a}$,$\vec{b}$,and $\vec{a}-\vec{b}$ are unit vectors and the angle between the two vectors $\vec{a}$ and $\vec{b}$ is $\theta$,then $\theta = $ . . . . . . .

If $a = i + 2j - 3k$ and $b = 3i - j + 2k$,find the angle between the vectors $a + b$ and $a - b$ in degrees.

If $\overline{a}+\overline{b}+\overline{c}=\overline{0}$ with $|\overline{a}|=3, |\overline{b}|=5$ and $|\overline{c}|=7$,then the angle between $\overline{a}$ and $\overline{b}$ is:

If the position vectors of $A$ and $B$ are $6i + j - 3k$ and $4i - 3j - 2k$ respectively,then the work done by the force $\vec{F} = i - 3j + 5k$ in displacing a particle from $A$ to $B$ is ............ $units$.