Question

Find the direction cosine of the line passing through the points $A(-4,2,3)$ and $B(1,3,-2)$

Answer 1

$A(-4,2,3)B(1,3,-2)$

D.r's of a line passing through $P(x_1,y_1,z_1)$ & $Q(x_2,y_2,z_2)$

$=(x_2-x_1),(y_2-y_1),(z_2-z_1)$

$D.C=\frac{x_2-x_1}{PQ},\frac{y_2-y_1}{PQ},\frac{z_2-z_1}{PQ}$

$PQ=AB=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$

$A=P;B=Q$

$x_1=-4;y_1=2;z_1=3$

$x_2=1;y_2=3;z_2=-2$

$D.r^{\prime }s=(x_2-x_1),(y_2-y_1),(z_2-z_1)$

$=1+4;3-2;-2-3$

$=5;1;-5$

$DC=\frac{5}{\sqrt{5^2+1^2+(-5{)}^2}}$; $\frac{1}{\sqrt{5^2+1^2+(-5{)}^2}}$; $\frac{-5}{\sqrt{5^2+1^2+(-5{)}^2}}$

$=\frac{5}{\sqrt{25+1+25}};\frac{1}{\sqrt{25+1+25}};\frac{-5}{\sqrt{25+1+25}}$

$=\frac{5}{\sqrt{51}};\frac{1}{\sqrt{51}};\frac{-5}{\sqrt{51}}$