Vector Algebra ...

The ratio in which the line joining $$(2,-4,3)$$ and $$(-4,5,-6)$$ is divided by the plane $$3x+2y+z-4=0$$ is 

A vector $$\overrightarrow { A } $$ points vertically downward(south)and $$\overrightarrow { B } $$ points towards east, then the vector product $$\overrightarrow { A } \times \overrightarrow { B } $$ is:

$$\bar{a}$$ and $$\bar{b}$$ are the position vectors of A and B respectively. Points P and Q divide AB, internally and externally in the same ratio 2:1 , then PQ is equal to 

Two vector $$A$$ and $$B$$ have equal magnitudes. Then the vector $$A+B$$ is perpendicular to 

The work done by the force $$\vec { F } = 2 \hat { i } - \hat { j } - \hat { \mathbf { k } }$$ in moung an object along the vector $$3 \hat { i } + 2 j - 5 \hat { k }$$ is

If  $$2\overline a  - 4\widehat i - 2\widehat j + \widehat k = 0$$ then find $$\overline a $$.

Let $$\vec{a}=\hat{i}+\hat{j}+\hat{k}$$ and $$\vec{b}$$ is a vector such that $$\vec{a}.\vec{b}=0$$ and $$\vec{a}\times \vec{b}=0$$. Then which of following is correct?

Given that $$\vec{ A } \times \vec{ B } =\vec{ B } \times \vec { C } =\vec { 0 } $$ if $$\vec{ A } \vec { B } \vec { C } $$ are not null vectors, Find the value of $$\vec{ A } \times \vec{ C } $$

Magnitude of vector $$3\hat { i } -12\hat { j } -4\hat { k } $$

$$\vec{r}  = \vec{x}\hat{i}+\vec{y}\hat{j}$$ is the equation of: