TS EAMCET · Maths · Three Dimensional Geometry
If \(\quad \overrightarrow{\mathbf{a}}=-\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{b}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}} \quad\) and \(\overrightarrow{\mathbf{c}}=-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), then the angle between \(2 \overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{c}}\) and \(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}\) is
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{3 \pi}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Now, \(\begin{aligned} 2 \overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{c}} & =2(-\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}})-(-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \\ & =\hat{\mathbf{j}}+\hat{\mathbf{k}} \end{aligned}\) and…
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