JEE Mains · Maths · STD 12 - 10. vector algebra
If vectors \(\overrightarrow{ a }_{1}= x \hat{ i }-\hat{ j }+\hat{ k }\) and \(\overrightarrow{ a }_{2}=\hat{ i }+ y \hat{ j }+ z \hat{ k }\) are collinear, then a possible unit vector parallel to the vector \(x \hat{i}+y \hat{j}+z \hat{k}\) is ...... .
- A \(\frac{1}{\sqrt{2}}(-\hat{ j }+\hat{ k })\)
- B \(\frac{1}{\sqrt{2}}(\hat{ i }-\hat{ j })\)
- C \(\frac{1}{\sqrt{3}}(\hat{ i }+\hat{ j }-\hat{ k })\)
- D \(\frac{1}{\sqrt{3}}(\hat{ i }-\hat{ j }+\hat{ k })\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\sqrt{3}}(\hat{ i }-\hat{ j }+\hat{ k })\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ a }_{1}\) and \(\overrightarrow{ a }_{2}\) are collinear so \(\frac{x}{1}=\frac{-1}{y}=\frac{1}{z}\) unit vector in direction of \(x \hat{i}+y \hat{j}+z \hat{k}=\pm \frac{1}{\sqrt{3}}(\hat{i}-\hat{j}+\hat{k})\)
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