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The direction cosines of the vector $3\mathbf{i}-4\mathbf{j}+5\mathbf{k}$ are
The position vectors of A and B are $2\mathbf{i}-9\mathbf{j}-4\mathbf{k}$ and $6\mathbf{i}-3\mathbf{j}+8\mathbf{k}$ respectively, then the magnitude of $\overrightarrow{AB}$ is
If the position vectors of P and Q are $(\mathbf{i}+3\mathbf{j}-7\mathbf{k})$ and $(5\mathbf{i}-2\mathbf{j}+4\mathbf{k}),$ then $|\overrightarrow{PQ}|$ is
If a is non zero vector of modulus a and m is a non-zero scalar, then ma is a unit vector if
The position vectors of the points A, B, C are $(2\mathbf{i}+\mathbf{j}-\mathbf{k}),$ $(3\mathbf{i}-2\mathbf{j}+\mathbf{k})$ and $(\mathbf{i}+4\mathbf{j}-3\mathbf{k})$ respectively. These points
The vectors $\overrightarrow{AB}=3\mathbf{i}+4\mathbf{k},$ and $\overrightarrow{AC}=5\mathbf{i}-2\mathbf{j}+4\mathbf{k}$ are the sides of a triangle ABC. The length of the median through A is
If the position vectors of the vertices A, B, C of a triangle ABC are $7\mathbf{j}+10\mathbf{k},$ $-\mathbf{i}+6\mathbf{j}+6\mathbf{k}$ and $-4\mathbf{i}+9\mathbf{j}+6\mathbf{k}$ respectively, the triangle is
The figure formed by the four points $\mathbf{i}+\mathbf{j}-\mathbf{k},\,\,\,2\mathbf{i}+3\mathbf{j},$ $3\mathbf{i}+5\mathbf{j}-2\mathbf{k}$ and $\mathbf{k}-\mathbf{j}$ is
ABC is an isosceles triangle right angled at A. Forces of magnitude $2\sqrt{2,}\,5$ and 6 act along $\overrightarrow{BC},\,\,\overrightarrow{CA}$ and $\overrightarrow{AB}$ respectively. The magnitude of their resultant force is
If ABCDEF is a regular hexagon and $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=\lambda \,\overrightarrow{AD},$ then $\lambda =$

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