Question

If line x-1/1=y/a=z+2/-1 lies in the plane 2x 3y 4z 10 = 0, then find value of a

Answer 1

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given (x1,y1,z1)(x1,y1,z1) is (−3,1,5)(−3,1,5) and

(x2,y2,z2)(x2,y2,z2) is (−1,2,5)(−1,2,5)

l1,m1,n1=−3,1,5l1,m1,n1=−3,1,5

and l1,m2,n2=−1,2,5

Hence the lines are coplanar.

The equation of the plane containing these lines is

(ie) (x+3)(5−10)−(y−1)(−15+5)+(2−5)(−6+1)(x+3)(5−10)−(y−1)(−15+5)+(2−5)(−6+1)

=> −5(x+3)+10(y−1)−5(z−5)−5(x+3)+10(y−1)−5(z−5)

=> −5x+10y−5z−30=0−5x+10y−5z−30=0

or 5x−10y+5z+30=05x−10y+5z+30=0

Hence this is the equation of the plane.




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