JEE Mains · Maths · STD 12 - 10. vector algebra
The set of all \(\alpha\), for which the vector \(\vec{a}=\alpha t \hat{i}+6 \hat{j}-3 \hat{k} \quad\) and \(\quad \vec{b}=t \hat{i}-2 \hat{j}-2 \alpha t \hat{k} \quad\) are inclined at an obtuse angle for all \(t \in \mathbb{R}\) is :
- A \([0,1)\)
- B \((-2,0]\)
- C \(\left(-\frac{4}{3}, 0\right]\)
- D \(\left(-\frac{4}{3}, 1\right)\)
Answer & Solution
Correct Answer
(C) \(\left(-\frac{4}{3}, 0\right]\)
Step-by-step Solution
Detailed explanation
\( \overrightarrow{\mathrm{a}}=\alpha t \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-3 \hat{\mathrm{k}} \) \( \overrightarrow{\mathrm{b}}=\mathrm{t}-2 \hat{\mathrm{j}}-2 \alpha \mathrm{t} \hat{\mathrm{k}} \)…
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