If \overline{r} \cdot(2 \overline{i}+3 \overline{j}+4 \overline{k})=5, \overline{r} \cdot(\overline{i}+\overline{j}-\overline{k})=7 are two planes and (16,-9,0) is a point common to both the planes then the vector equation of the line of intersection of the planes is \overline{r}=

Correct Answer is : (16−7λ)i+(6λ−9)j−λk

(16+7 \lambda) \overline{i}+(6 \lambda+9) \overline{j}+\lambda \overline{k}

(16-7 \lambda) \overline{i}+(6 \lambda-9) \overline{j}-\lambda \overline{k}

16 \overline{i}-9 \overline{j}+\lambda(\overline{i}-7 \overline{j}+6 \overline{k})

16 \overline{i}-9 \overline{j}+\lambda(6 \overline{i}-\overline{j}-7 \overline{k})

TS EAMCET 20-July-2022 Shift 1 Solved Paper

Section: Mathematics

Question : 33 of 160

Marks: +1, -0

If r⋅(2i+3j+4k)=5,r⋅(i+j−k)=7 are two planes and (16,−9,0) is a point common to both the planes then the vector equation of the line of intersection of the planes is r=

(16+7λ)i+(6λ+9)j+λk
(16−7λ)i+(6λ−9)j−λk
16i−9j+λ(i−7j+6k)
16i−9j+λ(6i−j−7k)

Validate

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