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If \(\vec{a}\) is nonzero vector such that its projections on the vectors \(2\overset{^}{\mathrm{i}}-\overset{^}{\mathrm…

Q1

If \(\vec{a}\) is nonzero vector such that its projections on the vectors \(2\overset{^}{\mathrm{i}}-\overset{^}{\mathrm{j}}+2\overset{^}{\mathrm{k}},\overset{^}{\mathrm{i}}+2\overset{^}{\mathrm{j}}-2\overset{^}{\mathrm{k}}\) and \(\overset{^}{k}\)are equal, then a unit vector along \(\vec{a}\) is:

[JEE Main 2025, 2 Apr (Shift 1)]

a

\(\frac{1}{\sqrt{155}}(-7\overset{^}{\mathrm{i}}+9\overset{^}{\mathrm{j}}+5\overset{^}{\mathrm{k}})\)

b

\(\frac{1}{\sqrt{155}}(-7\overset{^}{\mathrm{i}}+9\overset{^}{\mathrm{j}}-5\overset{^}{\mathrm{k}})\)

c

\(\frac{1}{\sqrt{155}}(7\overset{^}{\mathrm{i}}+9\overset{^}{\mathrm{j}}+5\overset{^}{\mathrm{k}})\)

d

\(\frac{1}{\sqrt{155}}(7\overset{^}{\mathrm{i}}+9\overset{^}{\mathrm{j}}-5\overset{^}{\mathrm{k}})\)

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