Find the equation of the plane passing through the line of intersection of the planes  and the point .



Asked by Topperlearning User | 27th Feb, 2015, 03:56: PM

Expert Answer:

The equation of the plane passing through the planes and  is: .

Also, the plane passing through the point.
Now, the required equation of the plane is:
 
rightwards double arrow open square brackets r with rightwards arrow on top times open parentheses j with hat on top minus 3 k with hat on top close parentheses minus 3 close square brackets minus 1 fifth open square brackets r with rightwards arrow on top times open parentheses i with hat on top plus 3 j with hat on top minus 2 k with hat on top close parentheses minus 2 close square brackets equals 0
rightwards double arrow 5 r with rightwards arrow on top times open square brackets open parentheses j with hat on top minus 3 k with hat on top close parentheses minus 3 close square brackets minus r with rightwards arrow on top times open square brackets open parentheses i with hat on top plus 3 j with hat on top minus 2 k with hat on top close parentheses minus 2 close square brackets equals 0
rightwards double arrow r with rightwards arrow on top times open square brackets open parentheses 0 minus 1 close parentheses i with hat on top plus open parentheses 5 minus 3 close parentheses j with hat on top minus open parentheses 15 minus 2 close parentheses k with hat on top close square brackets minus 15 plus 2 equals 0
rightwards double arrow r with rightwards arrow on top times open square brackets negative i with hat on top plus 2 j with hat on top minus 13 k with hat on top close square brackets minus 13 equals 0
rightwards double arrow r with rightwards arrow on top times open square brackets negative i with hat on top plus 2 j with hat on top minus 13 k with hat on top close square brackets equals 13

Answered by  | 27th Feb, 2015, 05:56: PM