The vector equation of the line passing through $\mathrm{P}(1,2,3)$ and $\mathrm{Q}(2,3,4)$ is

The vector equation of the line passing through $\mathrm{P}(1,2,3)$ and $\mathrm{Q}(2,3,4)$ is
  1. $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$
  2. $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}-\hat{k})$
  3. $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})$
  4. $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+6 \hat{j}+12 \hat{k})$

Solution

d.r. of line through PQ are $[(2,-1),(3,-2),(4,-3)]$ i.e. $(1,1,1)$ Hence required equation of line is $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$

Asked in: MHT CET 2021 (23 Sep Shift 2)

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