Question Type 4: Calculating the angle between a line and a plane Bootcamps

Find the angle between the line $r=t(1,1,1)$ and the plane $x+y+z=0$, expressing your answer in degrees.

Calculate the acute angle between the line given by $r=(3,2,1)+t(1,4,1)$ and the plane $2x+6y+z=1$, giving your answer in degrees to two decimal places.

Calculate the acute angle between the line $r=t(1,-1,0)$ and the plane $y+z=1$, in degrees.

Find the angle between the line $r=t(1,0,2)$ and the plane $5x+5y+z=2$, giving your answer in degrees to two decimal places.

Calculate the acute angle between the line $r=t(5,0,-2)$ and the plane $-x+2y+2z=3$, to two decimal places in degrees.

Determine the acute angle between the line $r=t(0,3,4)$ and the plane $3x-4y+12z=7$, in degrees to two decimal places.

Find the acute angle between the line $r=t(2,-1,3)$ and the plane $x+2y+2z=5$, giving the result in degrees to two decimal places.

Determine the acute angle between the line $r=t(2,2,3)$ and the plane $4x-4y+z=10$, giving the result in degrees to two decimal places.

Calculate the acute angle between the line $r=t(3,5,-2)$ and the plane $2x+3y-6z=4$, to two decimal places in degrees.

Determine the acute angle between the line $r=t(6,-3,2)$ and the plane $x-4y+8z=5$, giving your answer in degrees to two decimal places.

Determine the acute angle between the line $r=t(4,4,1)$ and the plane $7x-2y+3z=9$, giving the result to two decimal places.

Find the acute angle between the line $r=t(2,3,6)$ and the plane $3x+4y+12z=8$, giving your answer in degrees to two decimal places.