Three Dimension...

The equation of the plane passing through $$(a,b,c)$$ and parallel to the plane $$r.(\hat{i}+\hat{j}+\hat{k})=2$$ is,

Angle between the lines $$3x=6y=2z$$ and $$3x+2y+z-5=0=x+y-2z-3$$ is?

The points $$i + j + k, \, i + 2j, \, 2i+2j+k,\, 2i+3j+2k$$ are

If the dr's the line are $$(1+\lambda, 1-\lambda, 2)$$ and it makes an angle $${60}^{o}$$ with the Y-axis then $$\lambda$$ is

The line joining the points $$(-2, 1, -8)$$ and $$(a, b, c)$$ is parallel to the line whose direction ratios are $$6, 2, 3$$. The value of $$a, b, c$$ are

If a line has the direction ratio $$18, 12, 4 $$, then its direction cosines are:

The angle between the lines $$\dfrac {x - 1}{1} = \dfrac {y - 1}{1} = \dfrac {z - 1}{2}$$ and, $$\dfrac {x - 1}{-\sqrt {3} - 1} =  \dfrac {y - 1}{\sqrt {3} - 1} = \dfrac {z - 1}{4}$$ is

Equation of a line passing through the point $$\hat{i}+\hat{j}-\hat{k}$$ and parallel to the vector $$2\hat{i}+\hat{j}{+}2\hat{k}$$ is

If the points with position vectors $$60\hat{i}+3\hat{j},40\hat{i}-8\hat{j}$$ and $$a\hat{i}-52\hat{j}$$ are collinear then $$a$$ is equal to

Equation of a plane passing through the points $$A=\hat{i}+\hat{j}{+}\hat{k},\ B=\hat{j}{+\hat{k}}, C=\hat{k}$$ is