If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors and the maximum value of $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ is $k$,then $k(2|\vec{a}|^2+3|\vec{b}|^2-4|\vec{c}|^2) = $

The position vector of a point lying on the line joining the points whose position vectors are $\hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is:

Let $\overline{OA}=\overline{a}, \overline{OB}=\overline{b}$. If the vector along the angle bisector of $\angle AOB$ is given by $x \frac{\overline{a}}{|\overline{a}|}+y \frac{\overline{b}}{|\overline{b}|}$,then which of the following is true?

If $A(2, 3, 5)$,$B(1, 2, 3)$,$C(-5, 4, -2)$,and $D(1, 10, 10)$,then ...

Given the following expressions: $(A)$ $(a \times b) \cdot c$, $(B)$ $a \times (b \cdot c)$, $(C)$ $a \cdot (b \cdot c)$, $(D)$ $|a|(b \cdot c)$, $(E)$ $(a \cdot b) \times (b \cdot c)$. Which of the following statements is correct regarding their mathematical meaning?

In the given figure,which of the vectors are equal?