JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\vec{a}\) is nonzero vector such that its projections on the vectors \(2 \hat{i}-\hat{j}+2 \hat{k}, \hat{i}+2 \hat{j}-2 \hat{k}\) and \(\hat{k}\) are equal, then a unit vector along \(\vec{a}\) is:
- A \(\frac{1}{\sqrt{155}}(-7 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})\)
- B \(\frac{1}{\sqrt{155}}(-7 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}-5 \hat{\mathrm{k}})\)
- C \(\frac{1}{\sqrt{155}}(7 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})\)
- D \(\frac{1}{\sqrt{155}}(7 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}-5 \hat{\mathrm{k}})\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{155}}(7 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})\)
Step-by-step Solution
Detailed explanation
Let \(\overline{\mathrm{a}}=\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{a}_2 \hat{\mathrm{j}}+\mathrm{a}_3 \hat{\mathrm{k}}\) \(\mathrm{a}_1^2+\mathrm{a}_2^2+\mathrm{a}_3^2=1\) Let…
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