CUET · MATHS · PYQ PAPER 2023
The set of value of \(x\) for which the angle between the \(\vec{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}\) and \(\vec{b}=7 \hat{i}-2 \hat{j}+x \hat{k}\) is obtuse is :
- A \(\left(0, \frac{1}{2}\right)\)
- B \(\left(0, \frac{1}{3}\right)\)
- C \(\left(\frac{1}{2}, \frac{1}{3}\right)\)
- D \((0,1)\)
Answer & Solution
Correct Answer
(A) \(\left(0, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\vec{a} \cdot \vec{b} \((2x^2)(7) + (4x)(-2) + (1)(x) \(14x^2 - 8x + x \(14x^2 - 7x \(7x(2x - 1) \(x \in \left(0, \frac{1}{2}\right)\)
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