JEE Mains · Maths · STD 12 - 10. vector algebra
Let the vectors \((2+a+b) \hat{i}+(a+2 b+c) \hat{j}-(b+c) \hat{k}\) \((1+\mathrm{b}) \hat{i}+2 \mathrm{b} \hat{j}-\mathrm{b} \hat{k}\) and \((2+\mathrm{b}) \hat{i}+2 \mathrm{b} \hat{j}+(1-\mathrm{b}) \hat{k}\) \(\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{R}\) be co-planar. Then which of the following is true?
- A \(2 \mathrm{a}=\mathrm{b}+\mathrm{c}\)
- B \(2 \mathrm{~b}=\mathrm{a}+\mathrm{c}\)
- C \(3 \mathrm{c}=\mathrm{a}+\mathrm{b}\)
- D \(\mathrm{a}=\mathrm{b}+2 \mathrm{c}\)
Answer & Solution
Correct Answer
(B) \(2 \mathrm{~b}=\mathrm{a}+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
If the vectors are co-planner, \( \left|\begin{array}{ccc} a+b+2 & a+2 b+c & c b-c \\ b+1 & 2 b & -b \\ b+2 & 2 b & 1-b \end{array}\right|=0 \) Now \(R _{3} \rightarrow R _{3}- R _{2}, R _{1} \rightarrow R _{1}- R _{2}\) So…
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