Question

In R³

, find a general equation for the plane P₁which meets the plane P₂
​−3x+14y−2z=0 at a right angle and contains the line ℓ:x=(2,1,1)+t(2,8,6),t∈R Answer: one such general equation for P₁
is x+y+z=

Answer 1

To find a general equation for the plane P₁ in R³ that meets the plane P₂ at a right angle and contains the line ℓ:x=(2,1,1)+t(2,8,6), one such general equation for P₁ is x + y + z = 0.

Step-by-step explanation:

To find a general equation for the plane P₁ in R³ that meets the plane P₂ at a right angle and contains the line ℓ:x=(2,1,1)+t(2,8,6), we can use the normal vectors of the planes and the direction vector of the line.

The normal vector of plane P₂ is (-3, 14, -2) and the direction vector of line ℓ is (2, 8, 6). Since P₁ must meet P₂ at a right angle, the dot product of their normal vectors must be zero.

(a, b, c) · (-3, 14, -2) = 0

Solving this equation, we find that one such general equation for P₁ is x + y + z = 0.