Determine the distance D between the line l x 2514t y 1465

Determine the distance D between the line: l: x = 25+14t, y = 14-65t, z= 59+6t

and the plane P: 5x + 2y +10z = 98 Make sure to keep your answer exact,

The equation of line can be written as

(x-25)/14= (y-14)/-65=(z-59)/6=t

So, l=14, m=-65, n=6

The equation of plane is 5x+2y+10z-98=0

Comparing with ax+by+cz+d=0, we get

a=5, b=2, c=10

We know that the angle between them is given by

sin= (al+bm+cn)/(a²+b²+c²)(l²+m²+n²)

sin= (5*14)+(2*-65)+(10*6)/5²+2²+10²14²+(-65)²+6²

sin= (70-130+60)/1294457=0

Sin=sin0°

so, =0° Ans.