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If $\theta$ be the angle between the unit vectors a and b, then $\mathbf{a}-\sqrt{2}\,\mathbf{b}$ will be a unit vector if $\theta =$
If the angle between a and b be ${{30}^{o}}$, then the angle between 3 a and – 4 b will be
The angle between the vectors $\mathbf{i}-\mathbf{j}+\mathbf{k}$ and $\mathbf{i}+2\mathbf{j}+\mathbf{k}$ is
The position vector of vertices of a triangle ABC are $4\mathbf{i}-2\mathbf{j},\,\mathbf{i}+4\mathbf{j}-3\mathbf{k}$ and $-\mathbf{i}+5\mathbf{j}+\mathbf{k}$ respectively, then $\angle ABC=$
The value of x for which the angle between the vectors $\mathbf{a}=x\mathbf{i}-3\mathbf{j}-\mathbf{k},\,\,\mathbf{b}=2x\mathbf{i}+x\mathbf{j}-\mathbf{k}$ is acute and the angle between the vectors b and the axis of ordinate is obtuse, are
If a and b are unit vectors and $\mathbf{a}-\mathbf{b}$ is also a unit vector, then the angle between a and b is
If $\theta$ be the angle between two vectors a and b, then $\mathbf{a}.\mathbf{b}$ $\ge 0$ if
If $\mathbf{a}=\mathbf{i}+2\mathbf{j}-3\mathbf{k}$ and $\mathbf{b}=3\mathbf{i}-\mathbf{j}+2\mathbf{k},$ then the angle between the vectors $\mathbf{a}+\mathbf{b}$ and $\mathbf{a}-\mathbf{b}$ is
The value of x for which the angle between the vectors $\mathbf{a}=-\,3\mathbf{i}+x\mathbf{j}+\mathbf{k}$ and $\mathbf{b}=x\mathbf{i}+2x\mathbf{j}+\mathbf{k}$ is acute and the angle between b and x-axis lies between $\pi /2$ and $\pi $satisfy
The angle between the vectors $(2\mathbf{i}+6\mathbf{j}+3\mathbf{k})$ and $(12\mathbf{i}-4\mathbf{j}+3\mathbf{k})$ is

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