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Let u, v, w be such that |u| = 1, |v| = 2, |w| = 3. If the projection of v along u is equal to that of w along u and v, w are perpendicular to each other, then |u - v + w| equals

1. 14
2. √7
3. √14
4. 2

Correct answer: √14

Solution

The projection of v along u is given by the formula (v · u)u, and since the projections of v and w along u are equal, we can set up an equation involving their magnitudes. Given that v and w are perpendicular, we can use the Pythagorean theorem to find the magnitude of the vector u - v + w, leading to the result |u - v + w| = √14.

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