<PRE><B>Question 1084407</B>
1)  (U-3V) = (1;5)
2)  (-U+V) = (-5;3)
:
solve equation 1 for U
:
U = (1;5) + 3V
:
substitute in equation 2
:
-[(1;5) + 3V] + V= (-5;3)
:
(-1;-5) -3V + V = (-5;3)
:
-2V = (-4;8)
:
V = (2;-4)
:
U = (1;5) + 3(2;-4) = (7;-7)
:
U is (7,-7) and V is (2,-4)
:
we want the angle(theta) between vectors U and V
:
cos theta = (U . V) / |U| |V|, where . means dot product
:
U . V = 7*2 + -7*-4 = 42
|U| = square root(49 + 49) = square root(98) = 7 * square root(2)
|V| = square root(4 + 16) = square root(20) = 2 * square root(5)
:
cos theta = 42 / 14 * square root(2) * square root(5) = 3 / square root(10) = 0.9487
:
inverse cos 0.9487 = 18.4 degrees
:
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The angle between vectors U and V is 18.4 degrees
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