Question

- the vectors \( \bar{u} \) and \( \vec{v} \) are perpendiwlar. So, \( (\bar{v}-\bar{u}) \cdot \bar{u} \) are equal to: (A) 0 (B) \( 2\|\vec{u}\| \) (c) \( -\|\bar{u}\|^{2} \) (B) \( \|\bar{v}\|^{2} \

Answer 1

The expression (v-u).u represents the dot product between the vectors v-u and u. Give these vectors here are perpendicular, their dot product will be zero. Therefore, the correct answer is (A) 0.

The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. Expression (v-u).u represents the dot product between the vectors v-u and u.

Give these vectors here are perpendicular, their dot product will be zero. When two vectors are perpendicular, the cosine of the angle between them is zero, resulting in a dot product of zero.

In this case, (v-u) u indicating that the vectors v-u and u are orthogonal or perpendicular to each other.

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