AP EAMCET · Maths · Vector Algebra
If the angle \(\theta\) between the vectors \(\overrightarrow{\mathbf{a}}=2 x^2 \hat{\mathbf{i}}+4 x \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{b}}=7 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+x \hat{\mathbf{k}}\) is such that \(90^{\circ} < \theta < 180^{\circ}\), then \(x\) lies in the interval
- A \(\left(0, \frac{1}{2}\right)\)
- B \(\left(\frac{1}{2}, 1\right)\)
- C \(\left(1, \frac{3}{2}\right)\)
- D \(\left(\frac{1}{2}, \frac{3}{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(0, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
Given, \(\overrightarrow{\mathbf{a}}=2 x^2 \hat{\mathbf{i}}+4 x \hat{\mathbf{j}}+\hat{\mathbf{k}}\) \(\overrightarrow{\mathbf{b}}=7 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+x \hat{\mathbf{k}}\), also \(90^{\circ} So, \(\quad x \in\left(0, \frac{1}{2}\right)\)
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