Let P_1: x+y+2z-4=0 and P_2: 2x-y+3z+5=0 be two planes. Let A1,3,4 and B3,2,7 be two points in space. The equation of a third plane P_3 through the…

Question

Let P_1: x+y+2z-4=0 and P_2: 2x-y+3z+5=0 be two planes. Let A1,3,4 and B3,2,7 be two points in space. The equation of a third plane P_3 through the line of intersection of P_1 and P_2 and parallel to AB is

MARKS Content Team · Accepted Answer

Correct answer: (D) 3y+z-13=0. Equation of P_3 is P_1+λP_2=0 x1+2λ+y1-λ+z2+3λ-4+5λ=0 AB→=<2,-1,3> a normal vector to plane P_3 is <1+2λ,1-λ,2+3λ> If AB is parallel to P_3=0 ⇒21+2λ-11-λ+32+3λ=0 ⇒2+4λ-1+λ+6+9λ=0 ⇒14λ+7=0 ⇒λ=-1/2 Equation of required plane is 0+y×3/2+z1/2-13/2=0 i.e. 3y+z-13=0

Let $P_{1} : x + y + 2 z - 4 = 0$ and $P_{2} : 2 x - y + 3 z + 5 = 0$ be two planes. Let $A (1, 3, 4)$ and $B (3, 2, 7)$ be two points in space. The equation of a third plane $P_{3}$ through the line of intersection of $P_{1}$ and $P_{2}$ and parallel to $A B$ is

Solution

More Three Dimensional Geometry Questions

Let P1: x+y+2z-4=0 and P2: 2x-y+3z+5=0 be two planes. Let A1,3,4 and B3,2,7 be two points in space. The equation of a third plane P3 through the line of intersection of P1 and P2 and parallel to AB is

Solution

More Three Dimensional Geometry Questions

Let $P_{1} : x + y + 2 z - 4 = 0$ and $P_{2} : 2 x - y + 3 z + 5 = 0$ be two planes. Let $A (1, 3, 4)$ and $B (3, 2, 7)$ be two points in space. The equation of a third plane $P_{3}$ through the line of intersection of $P_{1}$ and $P_{2}$ and parallel to $A B$ is