Vector Angle and Operations (Jee Mains)

Mole Concept & Percentage Composition

Medium

Vector Angle and Operations

Let the angle $\theta ,0 < \theta < \frac{\pi }{2}$ between two unit vectors $\hat a$ and $\hat b$ be ${\sin ^{-1}}\left( {\frac{{\sqrt {65} }}{9}} \right)$ . 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

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