COMEDK · Maths · 33. Vector Algebra
If \(\mathrm{p}=\hat{i}+\hat{j}, \mathrm{q}=4 \hat{k}-\hat{j}\) and \(\mathrm{r}=\hat{i}+\hat{k}\), then the unit vector in the direction of \(3 \mathrm{p}+\mathrm{q}-2 \mathrm{r}\) is
- A \(\dfrac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})\)
- B \(\dfrac{1}{3}(\hat{i}-2 \hat{j}-2 \hat{k})\)
- C \(\dfrac{1}{3}(\hat{i}-2 \hat{j}+2 \hat{k})\)
- D \(\hat{i}+2 \hat{j}+2 \hat{k}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})\)
Step-by-step Solution
Detailed explanation
Given vectors are \(\vec{p} = \hat{i} + \hat{j}\), \(\vec{q} = -\hat{j} + 4\hat{k}\), and \(\vec{r} = \hat{i} + \hat{k}\). Calculate the vector \(\vec{v} = 3\vec{p} + \vec{q} - 2\vec{r}\): \(\vec{v} = 3(\hat{i} + \hat{j}) + (-\hat{j} + 4\hat{k}) - 2(\hat{i} + \hat{k})\)…
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