Having trouble with this one. In real-number multiplication, if uv_1 =uv_2 and u

Question

Having trouble with this one.

In real-number multiplication, if uv_1 =uv_2 and u 0, we can cancel the u and conclude that v_1 = v_2. Does the same rule hold for the dot product? That is, if u v_1 = u v_2 and u 0, can you conclude that v_1 =v_2? Give reasons for your answer. Choose the correct answer below. The conclusion v_1 = v_2 can be made. Let u = (2, 2, 2), v_1 = (3, 4, -5), and v_2 = (3, 4, -3). The dot product u v_1 = u v_2 is satisfied, and V_1 = V_2. The conclusion v_1 = v_2 cannot be made in general. It is only true if u v_1 = u v_2 = 0. The conclusion v_1 = v_2 cannot be made. Let u = (1, 1, 1), v_1 = (2, 3, -5>, and v_2 = (4,-1, -3). The dot product u v_1 = u v_2 is satisfied, but v_1 v_2. The conclusion v_1 = v_2 can be made because the dot product is defined using real-number multiplication.

Explanation / Answer

Answer is C

Because there may be more than 1 vectors satisying the expression u.v1=u.v2

u.v1=1*2+1*3+1*-5=0

u.v2=4-1-3=0

but v1 is not equal to v2

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