Three Dimensional Geometry · Mathematics · Class 12

If a line makes angles of $$90^{\circ}, 135^{\circ}$$ and $$45^{\circ}$$ with the $$x, y$$ and $$z$$ axes respectively, then its direction cosines are:

The angle between the lines $$2 x=3 y=-z$$ and $$6 x=-y=-4 z$$ is:

Find the vector and the cartesian equations of a line that passes through the point $$A(1,2,-1)$$ and parallel to the line $$5 x-25=14-7 y=35 z$$.

(a) Find the coordinates of the foot of the perpendicular drawn from the point $$P(0,2,3)$$ to the line $$\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$$.

OR

(b) Three vectors $$\vec{a} \cdot \vec{b}$$ and $$\vec{c}$$ satisfy the condition $$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$$. Evaluate the quantity $$\mu= \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$$, if $$|\vec{a}|=3,|\vec{b}|=4$$ and $$|\vec{c}|=2$$