TS EAMCET · Maths · Three Dimensional Geometry
If the vector \(19 \hat{\mathbf{i}}+22 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) bisects an angle between the vectors a and \(6 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}\), then the unit vector in the direction of \(\mathbf{a}\) is
- A \(\frac{1}{5}(4 \hat{\mathbf{i}}+3 \hat{\mathbf{k}})\)
- B \(\frac{1}{3}(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)
- C \(\frac{1}{3}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\)
- D \(\frac{1}{3}(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3}(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)
Step-by-step Solution
Detailed explanation
Let vector \(\mathbf{a}=a_1 \hat{\mathbf{i}}+a_2 \hat{\mathbf{j}}+a_3 \hat{\mathbf{k}}\) Now, vector bisector of angle between \(\mathbf{a}\) and \(6 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}\) is…
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