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

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• If the position vectors of A and B are $\mathbf{i}+3\mathbf{j}-7\mathbf{k}$ and $5\mathbf{i}-2\mathbf{j}+4\mathbf{k},$ then the direction cosine of $\overrightarrow{AB}$ along y-axis is

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• The position vectors of P and Q are $5\mathbf{i}+4\mathbf{j}+a\mathbf{k}$ and $-\mathbf{i}+2\mathbf{j}-2\mathbf{k}$ respectively. If the distance between them is 7, then the value of a will be

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• If $\vec{\lambda }$ is a unit vector perpendicular to plane of vector a and b and angle between them is $\theta$, then a . b will be

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• The area of the parallelogram whose diagonals are $\frac{3}{2}\mathbf{i}+\frac{1}{2}\mathbf{j}-\mathbf{k}$ and $2\mathbf{i}-6\mathbf{j}+8\mathbf{k}$ is

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