Let the equation of the plane, that passes through the point (1, 4, $$-$$3) and contains the line of intersection of the planes 3x $$-$$ 2y + 4z $$-$$ 7 = 0 and x + 5y $$-$$ 2z + 9 = 0, be $$\alpha$$x + $$\beta$$y + $$\gamma$$z + 3 = 0, then $$\alpha$$ + $$\beta$$ + $$\gamma$$ is equal to :
JEE · Math · previous-year question
- A.$$-$$23correct
- B.$$-$$15
- C.23
- D.15
Answer
A. $$-$$23
Explanation
3x $$-$$ 2y + 4z $$-$$ 7 + $$\lambda$$(x + 5y $$-$$ 2z + 9) = 0 (3 + $$\lambda$$)x + (5$$\lambda$$ $$-$$ 2)y + (4 $$-$$ 2$$\lambda$$)z + 9$$\lambda$$ $$-$$ 7 = 0 passing through (1, 4, $$-$$3) $$\Rightarrow$$ 3 + $$\lambda$$ + 20$$\lambda$$ $$-$$ 8 $$-$$ 12 + 6$$\lambda$$ + 9$$\lambda$$ $$-$$ 7 = 0 $$\Rightarrow$$ $$\lambda$$ = $${2 \over 3}$$ $$\Rightarrow$$ equation of plane is $$-$$11x $$-$$ 4y $$-$$ 8z + 3 = 0 $$\Rightarrow$$ $$\alpha$$ + $$\beta$$ + $$\gamma$$ = $$-$$23
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