determine the unit vector parallel to the cross products of the vector A equal 3i-5j +10k if B equal 6i+5j+2k
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Answer:
What is the unit vector parallel to the cross product of A x B where A=3i-5j+10k and B =6i+5j+2k?
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Well this is a fairly simple one because
a) you are asking for a unit vector which means we can ignore the magnitude of the cross product; a unit vector has magnitude 1. All we need to find is the direction.
b)Since the direction of a cross product is perpendicular to the plane containing the two vectors, the problem is largely a matter of finding that plane.
In accordance with the procedure given at
namely, given 2 vectors
u = u1i + u2j + u3k and
v= v1i + v2j + v3k,
the cross product is
(u2v3 - v2u3)i + (u3v1 - v3u1)j + (u1v2 - v1u2)k.
Plugging in the given coordinates, we have
((-5)*2 - 5*10)i + (10*6 - 2*3)j + (3*5 -6*(-5))k = -60i + 54j + 45k
To get the unit vector, we divide this by its magnitude, which is the square root of 60^2 + 54^2 + 45^2 = 3600 + 2916 + 2025 = 8541.
That square root is 92.42 to 2 decimal places. Which means that the unit vector you seek is approximately (-60i + 54j + 45k)/92.42, if I am not mistaken.