AP EAMCET · Maths · Three Dimensional Geometry
Angle between the planes \(\vec{r} \cdot(2 \hat{i}+4 \hat{j}-3 \hat{k})=5\) and \(\vec{r} \cdot(5 \hat{i}+3 \hat{j}+4 \hat{k})=7\) is
- A \(\cos ^{-1}\left(\frac{12}{13}\right)\)
- B \(\cos ^{-1}\left(\frac{6 \sqrt{2}}{13}\right)\)
- C \(\cos ^{-1}\left(\frac{3 \sqrt{2}}{13}\right)\)
- D \(\cos ^{-1}\left(\frac{6}{13}\right)\)
Answer & Solution
Correct Answer
(B) \(\cos ^{-1}\left(\frac{6 \sqrt{2}}{13}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \vec{r} \cdot(12 \hat{i}+4 \hat{j}-3 \hat{k})=5 \text { and } \vec{r} \cdot(5 \hat{i}+3 \hat{j}+4 \hat{k})=7 \\ & n_1=12 \hat{i}+4 \hat{j}-3 \hat{k} \text { and } n_2=5 \hat{i}+3 \hat{j}+4 \hat{k} \\ & \cos \theta=\left|\frac{n_1 \cdot…
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