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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 1 · Q25
Find the co-ordinates of the point on the line r =- j +3 k +λ(2 i -2 j + k ) such that the sum of co-ordinates is 3.
Find the co-ordinates of the point on the line $\displaystyle \vec{r}=-\hat{j}+3 \hat{k}+\lambda(2 \hat{i}-2 \hat{j}+\hat{k})$ such that the sum of co-ordinates is $\displaystyle 3$ .
Marking-scheme solution
$\displaystyle \vec{r}=-\hat{\jmath}+3 \hat{k}+\lambda\left(2 \hat{\imath}-2 \hat{\jmath}+\hat{k}\right)$
i.e. $\displaystyle \vec{r}=2 \lambda \hat{\imath}+(-2 \lambda-1) \hat{\jmath}+(\lambda+3) \hat{k}$
According to question,
$\displaystyle 2 \lambda+(-2 \lambda-1)+(\lambda+3)=3 \Rightarrow \lambda=1$
$\displaystyle \therefore \vec{r}=2 \hat{\imath}-3 \hat{\jmath}+4 \hat{k}$
Co-ordinates of the required point is $\displaystyle (2,-3,4)$.
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