Three Dimension...

The direction cosines of the perpendicular from the origin to the plane $$\displaystyle 3x  - y + 4z = 5$$ are

The equation of the right bisector plane of the segment joining $$(2,3,4)$$ and $$(6,7,8)$$ is

The line $$\dfrac{x-x_{1}}{0}=\dfrac{y-y_{1}}{1}=\dfrac{z-z_{1}}{2}$$ is:

If the direction cosines of the line joining the origin and a point at unit distance from the origin are $$\displaystyle \frac{1}{\sqrt{3}}$$, $$-\displaystyle \frac{1}{2}$$, $$\lambda$$    then value of $$\lambda$$ is?

Vector equation of the plane $$\vec{r}=\widehat{i}-\widehat{j}+\lambda (\widehat{i}+\widehat{j}+\widehat{k})+ \mu (\widehat{i}-2\widehat{j}+3\widehat{k})$$ in the scalar dot product form is

If $$\theta $$ is an angle given by $$\cos \theta $$  $$=$$ $$\displaystyle  \frac{\cos ^{2}\alpha+\cos ^{2}\beta +\cos ^{2}\gamma}{\sin ^{2}\alpha +\sin ^{2}\beta +\sin ^{2}\gamma }$$ where  $$\alpha $$, $$\beta $$, $$\gamma $$ are the angles made by a line with the positive directions of the axes of reference then the measure of $$\theta $$ is

If a line makes angles of $$60^{\circ}$$ and $$45^{\circ}$$ with the positive directions of the $$x$$-axis and $$y$$-axis respectively, then the acute angle between the line and the $$z$$-axis is

The equation of the plane passing through the line $$\displaystyle \frac{x - 1}{2} = \frac{y + 1} {-1} = \frac{z}{3}$$ and parallel to the direction whose direction numbers are $$3, 4, 2$$ is

If the points $$A(1,2,-1)$$, $$B(2,6,2)$$ and $$\displaystyle C\left ( \lambda,-2,-4 \right )$$ are collinear, then $$\displaystyle \lambda $$ is

$$ABC$$ is a triangle where $$A= \left ( 2,3,5 \right ),B= \left ( -1,3,2 \right ) $$ and $$C= \left (\lambda ,5,\mu   \right )$$. If the median through A is equally inclined with the axes, then