If the components of a=α i+β j+γ k along and perpendicular to b=i+j-k respectively, are 16/11(3 i+j-k) and 1/11(-4 i-5 j-17 k), then α²+β²+γ² is equal to:

Vector Algebra: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q77

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002

If the components of

\vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}

along and perpendicular to

\vec{b}=\hat{i}+\hat{j}-\hat{k}

respectively, are

\frac{16}{11}(3 \hat{i}+\hat{j}-\hat{k})

and

\frac{1}{11}(-4 \hat{i}-5 \hat{j}-17 \hat{k})

, then

\alpha^2+\beta^2+\gamma^2

is equal to:

JEE Main 2025 Vector Algebra Question with Solution (January Unspecified (session-level dataset), Q77) | JEE Arc