Suppose v_1, v_2, v_3 is an orthogonal set of vectors in {\mathbb R}^5 .
Let
w be a vector in {\mathrm{Span}}(v_1, v_2, v_3) such that

v_1 \cdot v_1 = 22, v_2 \cdot v_2 = 25.25, v_3 \cdot v_3 = 16 ,

w \cdot v_1 = 66, w \cdot v_2 = 101, w \cdot v_3 = 48 ,

thenw = v_1 + v_2
+ v_3 .

then

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