In R 3 , consider the planes P 1   : y = 0 and P 2   : x + z = 1 . Let P 3 , be a plane, different from P 1 and P 2 , which passes through the intersection of P 1 and P 2 . If the distance of the point 0 ,   1 ,   0 , from P 3 , is 1 , and the distance of a point ( α ,…

Question

In R 3 , consider the planes P 1 &#160; : y = 0 and P 2 &#160; : x + z = 1 . Let P 3 , be a plane, different from P 1 and P 2 , which passes through the intersection of P 1 and P 2 . If the distance of the point 0 , &#160; 1 , &#160; 0 , from P 3 , is 1 , and the distance of a point ( &#945; , &#160; &#946; , &#160; &#947; ) , from P 3 , is 2 , then which of the following relations is (are) true ?

Aicharya · Accepted Answer

P 1 : y = 0 P 2 : x + z = 1 P 3 : y + λ x + z - 1 = 0 ∴ β + λ α + γ - 1 1 + 2 λ 2 = ± 2 ∴ β + λ α + γ - 1 = ± 2 1 + 2 λ 2 1 - λ 1 + 2 λ 2 = ± 1 λ = - 2 λ ≠ 0 ∴ β - 2 α + γ - 1 = ± 2 3 2 α - β + 2 γ + 4 = 0 or 2 α - β + 2 γ - 8 = 0 .

In R 3 , consider the planes P 1   : y = 0 and P 2   : x + z = 1 . Let P 3 , be a plane, different…

Solution

In R 3 , consider the planes P 1 &#160; : y = 0 and P 2 &#160; : x + z = 1 . Let P 3 , be a plane, different…

Solution

In R 3 , consider the planes P 1 : y = 0 and P 2 : x + z = 1 . Let P 3 , be a plane, different…