If in triangle

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

If in triangle ABCABC , AB=u∣u∣−v∣v∣AB = \frac{\mathbf{u}}{|\mathbf{u}|} - \frac{\mathbf{v}}{|\mathbf{v}|} and AC=2u∣u∣AC = \frac{2\mathbf{u}}{|\mathbf{u}|} , where ∣u∣≠∣v∣|\mathbf{u}| \neq |\mathbf{v}| , then (1) 1+cos⁡2A+cos⁡2B+cos⁡2C=01 + \cos 2A + \cos 2B + \cos 2C = 0 (2) sin⁡A=cos⁡C\sin A = \cos C (3) projection of ACAC on BCBC is equal to BCBC (4) projection of ABAB on BCBC is equal to ABAB

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