The vector equation of any plane passing through the line of intersection of the planes \overline{r} \cdot \overline{m}_1=q_1 and \overline{r} \cdot \overline{m}_2=q_2 is given by \overline{r} \cdot (\overline{m}_1+\lambda-\overline{m}_2) =q_1+\lambda q_2 for \lambda \in \mathbb{R}. The vector equation of a plane passing through the point 2 \overline{i}-3 \overline{ {\j}}+\overline{ {\k}} and the line of intersection of the planes \overline{ {\r}} \cdot(\overline{ {\i}}-2 \overline{ {\j}}+3 \overline{ {\k}})=5 and \overline{ {\r}} \cdot(3 \overline{ {\i}}+\overline{ {\j}}-2 \overline{ {\k}})=7 is

Correct Answer is : r⋅(4i−j+k)=12

\overline{ {\r}} \cdot(-2 \overline{ {\i}}-3 \overline{ {\j}}+5 \overline{ {\k}})=-2

\overline{ {\r}} \cdot(7 \overline{ {\i}}-\overline{ {\k}})=19

\overline{ {\r}} \cdot(4 \overline{ {\i}}-\overline{ {\j}}+\overline{ {\k}})=12

\overline{ {\r}} \cdot(8 \overline{ {\i}}+5 \overline{ {\j}}-9 \overline{ {\k}})=16

AP EAPCET 19th May 2023 Shift 1 Solved Paper

Section: Mathematics

Question : 31 of 160

Marks: +1, -0

The vector equation of any plane passing through the line of intersection of the planes r⋅m1=q1 and r⋅m2=q2 is given by r⋅(m1+λ−m2)=q1+λq2 for λ∈ℝ. The vector equation of a plane passing through the point 2i−3j+k and the line of intersection of the planes r⋅(i−2j+3k)=5 and r⋅(3i+j−2k)=7 is

r⋅(−2i−3j+5k)=−2
r⋅(7i−k)=19
r⋅(4i−j+k)=12
r⋅(8i+5j−9k)=16

Validate

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