Find u*v if u=14j and v=i+4j
A. 56
B. -56
C. (1,56)
D. (0,56)
To find u*v, we need to multiply the scalar magnitudes with each other and then add the dot product of the two vectors.
u = 14j = (0, 14)
v = i + 4j = (1, 4)
The scalar magnitudes are:
|u| = sqrt(0^2 + 14^2) = 14
|v| = sqrt(1^2 + 4^2) = sqrt(17)
Now, find the dot product of u and v:
u.v = 0*1 + 14*4 = 56
Finally, multiply the scalar magnitudes with the dot product:
u*v = 14 * sqrt(17) * 56 = 56
Therefore, the answer is A. 56.