Three Dimension...

Let $$\overrightarrow{p}=3a{x}^{2}\hat{i}-2\left(x-1\right)\hat{j}$$ and $$\overrightarrow{q}=b\left(x-1\right)\hat{i}+x\hat{j}$$. If $$ab<0$$ then $$\overrightarrow{p}$$ and $$\overrightarrow{q}$$ are parallel for 

If $$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$$ are non-coplanar and $$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\alpha\overrightarrow{d}$$ ,  $$\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=\beta\overrightarrow{a}$$ then $$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=$$

If the angle between the line $$ x = \dfrac { y - 1 } { 2 } = \dfrac { z - 3 } { \lambda } $$ and the plane $$ x + 2 y + 3 z = 4 \text { is } \cos ^ { - 1 } \left( \sqrt { \frac { 5 } { 14 } } \right) $$, then $$ \lambda $$ equals:-

$$A=(-1, 2, -3), B=(5, 0, -6), C=(0, 4, -1)$$ are the vertices of a triangle. The d.c's of the internal bisector of $$\angle$$BAC are?

If the points whose position vectors are $$2i+j+k, 6i-j+2k$$ and $$14i-5j+pk$$ are collinear, then the value of p is?

The projection of a vector on three coordinate axes are $$ 6,-3, 2$$ respectively. The direction cosines of the vector are

The vector form of the equation of the line passing through points $$(3,4, 7)$$ and $$(5,1,6)$$ is-

If two lines $$x=2y+3, z=y+1$$ and $$x=4y+1, z=3y+2$$ makes an angle $$\theta$$ with each other, then $$\cos\theta$$ equals

The line perpendicular to the plane $$2x-y+5z=4$$ passing through the point $$(-1,0,1)$$ is ?

If a straight line makes an angle $${ cos }^{ -1 }\left( \frac { 1 }{ \sqrt { 3 }  }  \right) $$  with each of the positive $$x, y$$ and $$z$$-axis, a vector parallel to that line is