Let the position vectors of vertices A, B, and C of a triangle be 2i + 2j + k, i + 2j + 2k, and 2i + j + 2k re…

Question

Let the position vectors of vertices **A**, **B**, and **C** of a triangle be $$2\mathbf{i} + 2\mathbf{j} + \mathbf{k}$$, $$\mathbf{i} + 2\mathbf{j} + 2\mathbf{k}$$, and $$2\mathbf{i} + \mathbf{j} + 2\mathbf{k}$$ respectively. Let $$l_1$$, $$l_2$$, and $$l_3$$ be lengths of perpendiculars from the orthocenter to sides **AB**, **BC**, and **CA**. Then $$l_1^2 + l_2^2 + l_3^2$$ equals:

Accepted Answer

B. $$\frac{1}{2}$$

Answer

A. $$\frac{1}{5}$$

Answer

C. $$\frac{1}{4}$$

Answer

D. $$\frac{1}{3}$$

Answer & step-by-step solution

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