Line $L$ lies in the plane $x + 3 y - z = 9$ is perpendicular to line $\to r =^i +^j +^k + λ (2^i +^j -^k), λ \in R$ and passes through the point where plane meets the given line. Sum of coordinates of the point, where the line meets the $X Y$ plane is

Open in App

Solution

Vector perpendicular to $2^i +^j -^k$ and $^i + 3^j -^k$ is $(2^i +^j -^k) \times (^i + 3^j -^k) = 2^i +^j + 5^k$

Given the line $\to r =^i +^j +^k + λ (2^i +^j -^k), λ \in R$
Therefore, the coordinate of any point on the above line is $(1 + 2 λ, 1 + λ, 1 - λ)$

This point lines on the given plane.
$∴ (1 + 2 λ) + 3 (1 + λ) - (1 - λ) = 9 \Rightarrow λ = 1$
Point of intersection of plane with line $(3, 2, 0)$ and this is also the required point of intersection.

Suggest Corrections

Similar questions

P : x + 3 y - z = 9,

L : \to r =^i +^j +^k + λ (2^i +^j -^k)

P

L,

r = (^i +^j +^k) + α (2^i -^j + 4^k)

^i +^j - 2^k, 2^i -^j +^k

^i + 2^j +^k

\to r = 3^i -^j -^k + λ (2^i - 2^j +^k)

\to r

(^i + 2^j -^k) = 3

\to r =^i +^j + λ (2^i +^j + 4^k)

P (2, - 1, 3)

\to r =^i +^j -^k + λ (2^i - 2^j +^k)

\to r = (2^i -^j - 3^k) + μ (^i + 2^j + 2^k)

Join BYJU'S Learning Program