TS EAMCET · Maths · Vector Algebra
If \(P \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\) and \(4 \hat{\mathbf{i}}+13 \hat{\mathbf{j}}-18 \hat{\mathbf{k}}\) are the position vectors of three collinear points \(A, B\) and \(C\) respectively, then the vector in the direction of \(\mathbf{A B}\) of length \(|P|\) units is
- A \(\frac{2}{5 \sqrt{3}}(\hat{i}+5 \hat{j}-7 \hat{k})\)
- B \(\frac{1}{\sqrt{83}}(3 \hat{i}+5 \hat{j}-7 \hat{k})\)
- C \(\frac{1}{\sqrt{78}}(2 \hat{i}+5 \hat{j}-7 \hat{k})\)
- D \(\frac{1}{5 \sqrt{3}}(\hat{i}+5 \hat{j}-7 \hat{k})\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{5 \sqrt{3}}(\hat{i}+5 \hat{j}-7 \hat{k})\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{a}=P \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), \(\mathbf{b}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\) and \(\mathbf{c}=4 \hat{\mathbf{i}}+13 \hat{\mathbf{j}}-18 \hat{\mathbf{k}}\) Since, \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are…
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