Find the value of λ for which the planes vector r.(i + 2j + 3k) = 13

1.	Find the value of λ for which the planes vector r.(i + 2j + 3k) = 13 and vector r.(λi + 2j - 7k) = 9 are perpendicular to each other.
Answer» We know that two plane vector(r.n₁) = q₁ and vector(r.n₁) = q₂ are perpendicular to each other if and only if vector(n₁.n₂) = 0 Here, vector n₁ = (i + 2j + 3k) and vector n₂ = (i + 2j - 7k) Given that planes are perpendicular to each other So, vector(n₁.n₂) = 0 (i + 2j + 3k).(λi + 2j - 7k) = 0 1 x λ + 2 x 2 + 3 x -7 = 0 λ = 17 Hence, require value of λ is 17

Find the value of λ for which the planes vector r.(i + 2j + 3k) = 13 and vector r.(λi + 2j - 7k) = 9 are perpendicular to each other.

Answer»

We know that two plane vector(r.n₁) = q₁ and vector(r.n₁) = q₂ are perpendicular to each other if and only if vector(n₁.n₂) = 0

Here, vector n₁ = (i + 2j + 3k) and vector n₂ = (i + 2j - 7k)

Given that planes are perpendicular to each other

So, vector(n₁.n₂) = 0

(i + 2j + 3k).(λi + 2j - 7k) = 0

1 x λ + 2 x 2 + 3 x -7 = 0

λ = 17

Hence, require value of λ is 17