Answer
(a) A vector from any point on the line towards the point to want to find the distance from then find $\vec{P_0P_1}$
The distance from a point to a line can be calculated as:
$\frac{|\vec{P_0P_1} \times l|}{|l|}$
(b) To find the distance from point $A(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$, use the following formula:
$D=\dfrac{|ax_1+by_1+cz_1|}{\sqrt {a^2+b^2+c^2}}$
(c) The distance between two lines is defined as the perpendicular distance between them , therefore the two lines must be parallel to each other . To find the distance, first we need to find the slope $m$ of the lines, then find the opposite reciprocal of $m$ , this will the slope of the new line perpendicular to both lines, then we find the intersection $I_1$ and $I_2$ of the new line to the old lines, last we apply the distance formula from $I_1$ to $I_2$ .
Work Step by Step
(a) A vector from any point on the line towards the point to want to find the distance from then find $\vec{P_0P_1}$
The distance from a point to a line can be calculated as:
$\frac{|\vec{P_0P_1} \times l|}{|l|}$
(b) To find the distance from point $A(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$, use the following formula:
$D=\dfrac{|ax_1+by_1+cz_1|}{\sqrt {a^2+b^2+c^2}}$
(c) The distance between two lines is defined as the perpendicular distance between them , therefore the two lines must be parallel to each other . To find the distance, first we need to find the slope $m$ of the lines, then find the opposite reciprocal of $m$ , this will the slope of the new line perpendicular to both lines, then we find the intersection $I_1$ and $I_2$ of the new line to the old lines, last we apply the distance formula from $I_1$ to $I_2$ .
