YESPYQ Start Practice
JEEMaths

If \(\vec{a}\) is nonzero vector such that its projections on the vectors \(2\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\ma…

Q1
PYQ

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

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

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 & explanation — PYQ Pass

Options are free to see. Unlock the correct answer and full explanation with Pass.

Unlock · ₹149
← Previous questionNext question →

Practice more JEE Maths PYQs

See every question on Vector Algebra, or browse the full JEE question bank.

See all questions on Vector Algebra →

More JEE Maths PYQs

MathsLet \(\vec{a}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{b}=\vec{a} \times(\hat{i}-2 \hat{k})\) and…MathsLet \(\vec{a}=\hat{i}+2\hat{j}+\hat{k}\) and \(\vec{b}=2\hat{i}+\hat{j}-\hat{k}\). Let \(\…Maths\(\vec{a}=2\hat{i}-\hat{j}+3\hat{k},\overset{⇀}{b}=3\hat{i}-5\hat{j}+\hat{k}If\vec{a}\time…MathsLet \(\vec{a}=\sqrt{7 } \hat{\imath}+\hat{\jmath}-\hat{k}\) and \(\vec{b}=\hat{j}+2 \hat{k…MathsVectors with position vector \(A= \quad 2 \hat{i}+3 n \hat{j}+2 \hat{k} \quad B=\) \(2 \ha…Maths\(\vec{a}=2\hat{i}-\hat{j}+3\hat{k},\overset{⇀}{b}=3\hat{i}-5\hat{j}+\hat{k}If\vec{a}\time…