Statement 1: Line `(x-1)/1=(y-0)/2=(z2)/(-1)`lies in the plane `2x-3y-4z-10=0.`Statement 2: if line ` vec r= vec a+lambda vec b`lies in the plane ` vec rdot vec c=n(w h e r en`is scalar`),t h e n vec bdot vec c=0.`A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.C. Statement 1 is true and Statement 2 is false.D. Statement 1 is false and Statement 2 is true.

Statement 1: Line `(x-1)/1=(y-0)/2=(z2)/(-1)`lies in the plane `2x-3y-

1.	Statement 1: Line `(x-1)/1=(y-0)/2=(z2)/(-1)`lies in the plane `2x-3y-4z-10=0.`Statement 2: if line ` vec r= vec a+lambda vec b`lies in the plane ` vec rdot vec c=n(w h e r en`is scalar`),t h e n vec bdot vec c=0.`A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.C. Statement 1 is true and Statement 2 is false.D. Statement 1 is false and Statement 2 is true.
Answer» Correct Answer - c Statement 2 is true as when the line lies in the plane, vector `vecb` along which the line is directed is perpendicular to the normal `vecc` of the plane, but it does not explain Statement 1 as for `vecb * vecc= 0`, the line may be parallel to the plane. However, Statement 1 is correct as any point on the line `(t+1, 2t, -t-2)` lies on the plane for `t in R`.