if vector U= (1,-3,-2) and vector V= (4,-5,3) find | u+v-5j |
assuming j = (0,1,0) just do the arithmetic.
This can be done mentally to get u+v-5j = (5,-7,1)
now just take the magnitude of that
u + v = 5 i - 8 j + 1 k
5 j = 0 i + 5 j + 0 k
u + v - 5 j = 5 i - 13 j + 1 k
To find |u+v-5j|, we need to compute the magnitude (or length) of the vector u + v - 5j.
First, let's find the vector u + v by adding the corresponding components:
u + v = (1 + 4, -3 + (-5), -2 + 3) = (5, -8, 1)
Next, subtracting 5j from u + v means subtracting 5 times the vector j:
u + v - 5j = (5, -8, 1) - 5(0, 1, 0) = (5, -8, 1) - (0, 5, 0) = (5 - 0, -8 - 5, 1 - 0) = (5, -13, 1)
Finally, we can find the magnitude using the formula |a| = sqrt(a1^2 + a2^2 + a3^2):
|u + v - 5j| = sqrt((5^2) + (-13^2) + (1^2)) = sqrt(25 + 169 + 1) = sqrt(195) ≈ 13.96
Therefore, |u+v-5j| is approximately 13.96.