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Find the vector equation of a line passing through two points (-5,3,1) and (4,-3,2).(a) \((-5+λ) \hat{i}+(3+λ)\hat{j}+(1-λ) \hat{k}\)(b) \((-5+λ) \hat{i}+(3+6λ)\hat{j}+(1+λ) \hat{k}\)(c) \((5+7λ) \hat{i}+(8+6λ)\hat{j}+(3-5λ) \hat{k}\)(d) \((-5+9λ) \hat{i}+(3-6λ)\hat{j}+(1+λ) \hat{k}\)I have been asked this question at a job interview.I would like to ask this question from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12

Answer»

Right answer is (d) \((-5+9λ) \HAT{i}+(3-6λ)\hat{j}+(1+λ) \hat{K}\)

Explanation: Consider the POINTS A(-5,3,1) and B(4,-3,2)

LET \(\vec{a} \,and\, \vec{b}\) be the position vectors of the points A and B.

∴\(\vec{a}=-5\hat{i}+3\hat{j}+\hat{k}\)

\(\vec{b}=4\hat{i}-3\hat{j}+2\hat{k}\)

∴\(\vec{r}=-5\hat{i}+3\hat{j}+\hat{k}+λ(4\hat{i}-3\hat{j}+2\hat{k}-(-5\hat{i}+3\hat{j}+\hat{k}))\)

=-\(5\hat{i}+3\hat{j}+\hat{k}+λ(9\hat{i}-6\hat{j}+\hat{k})\)

=\((-5+9λ) \hat{i}+(3-6λ)\hat{j}+(1+λ) \hat{k}\)


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