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Statement 1: Line (x-1)/1=(y-0)/2=(z+2)/...

Statement 1: Line `(x-1)/1=(y-0)/2=(z+2)/(-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 r. vec c=n` (where `n` is scalar),then `vec b. 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.

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.

Text Solution

Verified by Experts

The correct Answer is:
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`.
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