Lines & Planes in Space

What is the equation of line that is parallel to the vector <1,2,3> and passes through the point (3,2,1)?

• r(t) = <3,2,1> +t <1,2,3>

• r(t) = <1,2,3> + t <3,2,1>

• r(t) = < -2,0,2 > + t < -2,0,2 >

• r(t) = < 2,0,-2 > + t < 2,0,-2 >

What is the equation of plane that is perpendicular to the vector <1,2,3> and passes through the point (3,2,1)?

• x + 2y +3z = 10

• x + 2y +3z = 6

• x + 2y +3z = 0

• x + 2y +3z = 14

Find the distance of point P(2,1,0) to the line r(t) = <3,4,1> + t <2,0,-2>.

• $\sqrt{88}$

• $\sqrt{8}$

• $\sqrt{11}$

• $0$

Find the distance of the point (2,1,0) to the plane 2x + 3y - z = 4.

• $\sqrt{\frac{285}{14}}$

• $-\sqrt{\frac{285}{14}}$

• $-\frac{3}{\sqrt{14}}$

• $\frac{3}{\sqrt{14}}$

Find the intersection of the line
r(t) = <2,1,5> + t<3,4,-3>
with the plane 3x + 4y - 3z = 7.

• No intersection

•  $\left(\frac{52}{17},\ \frac{41}{17},\ \frac{67}{17}\right)$  

• r(t) = <2,1,5> + t<3,4,-3>

• 3x + 4y - 3z = 7

Find the intersection between the two planes 2x + 3y - z = 0 and x + 3y + z = 1.

• No intersection

• (1,0,-1)

• $r\left(t\right)=<-1,\ \frac{2}{3},\ 0>+\ t<2,-1,1>$

• x - 2z = -1

Find the angle (in radian) between the two planes 2x + 3y - z = 0 and x + 3y + z = 1.

• 0.25

• 0.51

• 0.56

• 0.63