1
Question
Find the direction ratio of the plane passing through the points
R(2, 5, – 3), S(– 2, – 3, 5) and T(5, 3,– 3).
Find the direction ratio of the plane passing through the points
R(2, 5, – 3), S(– 2, – 3, 5) and T(5, 3,– 3).
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Solution
The correct option is A (2,3,4)
Using three point equation,
⎛⎜⎝x−2y−5z+3−2−2−3−55+35−23−5−3+3∣∣
∣
∣∣=0C2⇒C2−2C1C3⇒C3+2C1⎛⎜
⎜
⎜
⎜⎝x−2y−5−2(x−2)z+3+2(x−2)−4003−86∣∣
∣
∣
∣∣=0Expanding through R2, we get4(4x+6y+8z−14) =02x+3y+4z−7 =0
comparing the above equation to the general form, we get
a = 2
b = 3
c = 4
Using three point equation,
⎛⎜⎝x−2y−5z+3−2−2−3−55+35−23−5−3+3∣∣ ∣ ∣∣=0C2⇒C2−2C1C3⇒C3+2C1⎛⎜ ⎜ ⎜ ⎜⎝x−2y−5−2(x−2)z+3+2(x−2)−4003−86∣∣ ∣ ∣ ∣∣=0Expanding through R2, we get4(4x+6y+8z−14) =02x+3y+4z−7 =0
comparing the above equation to the general form, we get
a = 2
b = 3
c = 4