Let the angle θ, 0 < θ < (π)/2, be the angle between two unit vectors a and b, and θ = sin ⁻¹((√(65))/9). If the vector c = 3a + 6b + 9(a × b), then the value of 9(c · a) - 3(c · b) is:

Vector Algebra: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q194

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

Let the angle

\theta

0 < \theta < \frac{\pi}{2}

, be the angle between two unit vectors

\hat{a}

and

\hat{b}

, and

\theta = \sin^{-1}\left(\frac{\sqrt{65}}{9}\right)

. If the vector

\vec{c} = 3\hat{a} + 6\hat{b} + 9(\hat{a} \times \hat{b})

, then the value of

9(\vec{c} \cdot \hat{a}) - 3(\vec{c} \cdot \hat{b})

is: