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If $|\mathbf{a}+\mathbf{b}|\,\,>\,\,|\mathbf{a}-\mathbf{b}|,$ then the angle between a and b is
If a, b, c are three vectors such that $\mathbf{a}=\mathbf{b}+\mathbf{c}$ and the angle between b and c is $\pi /2,$ then (Note : Here $a=\,\,|\mathbf{a}|,\,\,b=\,|\,\mathbf{b}|,\,\,c=\,|\mathbf{c}|)$
If the angle between the vectors a and b be $\theta$ and $\mathbf{a}\,.\,\mathbf{b}=\cos \theta ,$ then the true statement is
If the vector $\mathbf{i}+\mathbf{j}+\mathbf{k}$ makes angles $\alpha ,\,\beta ,\,\gamma $with vectors $\mathbf{i},\,\mathbf{j},\mathbf{k}$respectively, then
${{(\mathbf{r}\,.\,\mathbf{i})}^{2}}+{{(\mathbf{r}\,.\,\mathbf{j})}^{2}}+{{(\mathbf{r}\,.\,\mathbf{k})}^{2}}=$
The value of b such that scalar product of the vectors $(\mathbf{i}+\mathbf{j}+\mathbf{k})$ with the unit vector parallel to the sum of the vectors $(2\mathbf{i}+4\mathbf{j}-5\mathbf{k})$ and $(b\mathbf{i}+2\mathbf{j}+3\mathbf{k})$ is 1, is
If a unit vector lies in yz–plane and makes angles of ${{30}^{o}}$ and ${{60}^{o}}$ with the positive y-axis and z-axis respectively, then its components along the co-ordinate axes will be
If $\overrightarrow{{{F}_{1}}}=\mathbf{i}-\mathbf{j}+\mathbf{k},$ $\overrightarrow{{{F}_{2}}}=-\mathbf{i}+2\mathbf{j}-\mathbf{k},$ $\overrightarrow{{{F}_{3}}}=\mathbf{j}-\mathbf{k},$ $\vec{A}=4\mathbf{i}-3\mathbf{j}-2\mathbf{k}$ and $\vec{B}=6\mathbf{i}+\mathbf{j}-3\mathbf{k},$ then the scalar product of $\overrightarrow{{{F}_{1}}}+\overrightarrow{{{F}_{2}}}+\overrightarrow{{{F}_{3}}}$and $\overrightarrow{AB}$ will be
If the moduli of a and b are equal and angle between them is ${{120}^{o}}$ and $\mathbf{a}\,.\,\mathbf{b}=-\,8,$ then | a | is equal to
If $|\mathbf{a}|\,\,=3,\,\,\,|\mathbf{b}\,\,|\,\,=4$ and the angle between a and b be ${{120}^{o}}$, then $|4\mathbf{a}+3\mathbf{b}|\,\,=$

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