vectors-m

Related Questions

• For any three non-zero vectors ${{r}_{1}},\,{{r}_{2}}$ and ${{r}_{3}}$, $\begin{vmatrix} {{r}_{1}}\,.\,{{r}_{1}} & {{r}_{1}}\,.\,{{r}_{2}} & {{r}_{1}}\,.\,{{r}_{3}} \\ {{r}_{2}}\,.\,{{r}_{1}} & {{r}_{2}}\,.\,{{r}_{2}} & {{r}_{2}}\,.\,{{r}_{3}} \\ {{r}_{3}}\,.\,{{r}_{1}} & {{r}_{3}}\,.\,{{r}_{2}} & {{r}_{3}}\,.\,{{r}_{3}} \\ \end{vmatrix}=0$. Then which of the following is false

  ---

• Let a and b be two non-collinear unit vectors. If $\mathbf{u}=\mathbf{a}-(\mathbf{a}\,.\,\mathbf{b})\,\mathbf{b}$ and $\mathbf{v}=\mathbf{a}\times \mathbf{b},$ then | v | is

  ---

• The unit vector perpendicular to the vectors $6\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ and $3\mathbf{i}-6\mathbf{j}-2\mathbf{k},$ is

  ---

• A unit vector perpendicular to the plane determined by the points (1, – 1, 2), (2, 0, – 1) and (0, 2, 1) is

  ---

• If $\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0,$ where a, b and c are coplanar vectors, then for some scalar k

  ---