vectors-m

Related Questions

• 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

  ---

• If the position vectors of the vertices of a triangle be $6\mathbf{i}+4\mathbf{j}+5\mathbf{k},\,\,\,4\mathbf{i}+5\mathbf{j}+6\mathbf{k}$ and $5\mathbf{i}+6\mathbf{j}+4\mathbf{k},$ then the triangle is

  ---

• If the vectors $\mathbf{i}-3\mathbf{j}+2\mathbf{k}$, $-\mathbf{i}+2\mathbf{j}$ represents the diagonals of a parallelogram, then its area will be

  ---

• If $|\mathbf{a}|=|\mathbf{b}|=1$ and $\mathbf{|a}+\mathbf{b}|=\sqrt{3}$, then the value of $(3\mathbf{a}-4\mathbf{b}).(2\mathbf{a}+5\mathbf{b})$ is

  ---

• Let $\alpha ,\,\,\beta ,\,\,\gamma $ be distinct real numbers. The points with position vectors $\alpha \mathbf{i}+\beta \mathbf{j}+\gamma \mathbf{k},\,\,\beta \mathbf{i}+\gamma \mathbf{j}+\alpha \mathbf{k},\,\,\gamma \mathbf{i}+\alpha \mathbf{j}+\beta \mathbf{k}$

  ---