CUET · MATHS · PYQ PAPER 2023
The vector equation of the line joining the points \((-2,-3,-4)\) and \((1,-2,4)\) is :
- A \(\vec{r}=(-2 \hat{i}-3 \hat{j}-4 \hat{k})+\lambda(\hat{i}-2 \hat{j}+4 \hat{k})\)
- B \(\vec{r}=(2 \hat{i}+3 \hat{j}+4 \hat{k})+\lambda(3 \hat{i}-\hat{j}+8 \hat{k})\)
- C \(\vec{r}=(-2 \hat{i}-3 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+\hat{j}+8 \hat{k})\)
- D \(\vec{r}=(2 \hat{i}+3 \hat{j}+4 \hat{k})+\lambda(3 \hat{i}+\hat{j}+8 \hat{k})\)
Answer & Solution
Correct Answer
(C) \(\vec{r}=(-2 \hat{i}-3 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+\hat{j}+8 \hat{k})\)
Step-by-step Solution
Detailed explanation
Let \(\vec{a} = -2 \hat{i} - 3 \hat{j} - 4 \hat{k}\) and \(\vec{b} = \hat{i} - 2 \hat{j} + 4 \hat{k}\). Direction vector \(\vec{d} = \vec{b} - \vec{a} = (1 - (-2)) \hat{i} + (-2 - (-3)) \hat{j} + (4 - (-4)) \hat{k} = 3 \hat{i} + \hat{j} + 8 \hat{k}\). Vector equation:…
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