AP EAMCET · PHYSICS · Mathematics in Physics
The dot product of unit vectors \(\hat{n}_1\) and \(\hat{n}_2\) that are parallel to \(5 \hat{i}+12 \hat{j}\) and \(3 \hat{i}+4 \hat{j}\) respectively is
- A \(\frac{63}{65}\)
- B \(63\)
- C \(\frac{63}{4225}\)
- D \(\frac{63}{845}\)
Answer & Solution
Correct Answer
(A) \(\frac{63}{65}\)
Step-by-step Solution
Detailed explanation
We have, \(\hat{\mathrm{n}}_1 \cdot \hat{\mathrm{n}}_2\) \(=\frac{1}{13}(5 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}) \cdot \frac{1}{5}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}})=\frac{1}{65}(15+48)=\frac{63}{65}\)
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