JEE Advance - Mathematics (1999 - No. 12)
Let $$u$$ and $$v$$ be units vectors. If $$w$$ is a vector such that $$w + \left( {w \times u} \right) = v,$$ then prove that $$\left| {\left( {u \times v} \right) \cdot w} \right| \le 1/2$$ and that the equality holds if and only if $$u$$ is perpendicular to $$v .$$
The magnitude of the scalar triple product (u x v) . w is always less than or equal to 1/4.
The vectors u and v are always parallel.
The magnitude of the scalar triple product (u x v) . w is always greater than 1/2.
The magnitude of the scalar triple product (u x v) . w is always less than or equal to 1/2 and equality holds if and only if u is perpendicular to v.
The equality |(u x v) . w| = 1/2 holds if and only if u and v are parallel.
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