Find the equation of the plane through the point 2i^+j^-k^ and passing through the line of intersection of the planes - Maths -

Question

Find the equation of the plane through the point 2 i ^ + j ^ - k ^
and passing through the line of intersection of the planes r
→ · i ^ + 3 j ^ - k ^ = 0   and   r →
· j ^ + 2 k ^ = 0

Global Expert · Accepted Answer

The equation of the plane passing through the line of intersection of the given planes isr→
 i^+3 j^-k^+λ r→
 j^+2 k^=0 r→
 i^+3+λ j^+-1+2λk^=0
 1This passes through 2 i^+j^-k^
 So,2 i^+j^-k^ i^+3+λ j^+-1+2λk^=0⇒2+3+λ+1-2λ=0⇒λ=6Substituting this in (1), we getr→
 i^+3+6 j^+-1+12k^=0⇒r→
 i^+9 j^+11 k^=0

Find the equation of the plane through the point 2 i ^ + j ^ - k ^ and passing through the line of intersection of the planes r → · i ^ + 3 j ^ - k ^ = 0 and r → · j ^ + 2 k ^ = 0 .

Find the equation of the plane through the point $2 \hat{i} + \hat{j} - \hat{k}$ and passing through the line of intersection of the planes $\vec{r} \cdot (\hat{i} + 3 \hat{j} - \hat{k}) = 0 and \vec{r} \cdot (\hat{j} + 2 \hat{k}) = 0 .$