Vector Algebra ...

If $$\vec{a}, \vec{b}, \vec{c}$$ are three non-coplanar vectors such that $$\vec{d}\cdot \vec{a}=\vec{d}\cdot \vec{b}=\vec{d}\cdot \vec{c}=0$$, then $$\vec{d}$$ is :-

If $$\overline {OA}=i+j+k, \overline {AB}=3i-2j+k,\overline {BC}=i+2j-2k$$ and $$\overline {CD}=2i+j+3k $$ then find the vector $$\overline{OD}$$.

The value of $$\bar {a} \times (\bar {b}+\bar {c})+\bar {b}\times (\bar {c}+\bar {a})+\bar {c}\times (\bar {a}+\bar {b})=$$

Let $$\vec{a},\vec{b}$$ and $$\vec{c}$$ be three non-zero vectors such that no two of these are collinear. If the vector $$\vec{a}+2\vec{b}$$ is collinear with $$\vec{c}$$ and $$\vec{b}+3\vec{c}$$ is collinear with $$\vec{a}(\lambda$$ being some non-zero scalar), then $$\vec{a}+2\vec{ b}+6\vec{c}$$ equals

The $$P.V.'s$$ of the vertices of a $$\triangle ABC$$ are $$\bar {i}+\bar {j}+\bar {k}, 4\bar {i}+\bar {j}+\bar {k}, 4\bar {i}+5\bar {j}+\bar {k}$$. The $$P.V.$$ of the circumcentre of $$\triangle ABC$$ is

Component of $$\vec{a}=\hat{i}-\hat{j}-\hat{k}$$ perpendicular to the vector $$\vec{b}=2\hat{i}+\hat{j}-\hat{k}$$ is?

If $$a^b=b^c=ab$$, then $$b+c$$ always equals?

$$\overline a  = \overline i  - \overline k ,\overline b  = x\overline i  + \overline j  + (1 - x)\overline k $$ and $$\overline c  = y\overline i  + \lambda \overline j  + (1 + x - y)\overline k $$ then $$\left[ {\overline a \overline b \overline c } \right]$$ depends on:-

$$A(1, -1, -3)$$, $$B(2, 1, -2)$$ & $$C(-5, 2, -6)$$ are the position vectors of the vertices of a triangle ABC. The length of the bisector of its internal angle at A is?

Let P, Q, R and S be the points on the plane with position vectors $$-2\hat{i}-\hat{j}, 4\hat{i}, 3\hat{i}+3\hat{j}$$ and $$-3\hat{i}+2\hat{j}$$ respectively. the quadrilateral PQRS must be a.