What is the magnitude of the following vector v=3i - 2j?
Answer:
Is it
|v| = sqrt(3^2+(-2)^2)
|v| = sqrt(13)
the squareroot of 13
Actually i and j are mathematical symbols for the sqrt of (-1)
So the magnitude in this case is the sum of the two:
which is i or j which is sqrt of (-1)
The other two answers you received are based on the assumption that the vectors create a right triangle which is not necessarily true.
The magnitude of v is the square root of 13. The vector v has a magnitude of 3 in the i(or x) direction and -2 in the j(or y) direction. The magnitude is the square root of the sum of the squares of the two components. This assumes that the vector voltage is expressed using the convention that 3i is the real component of the voltage and -2j is the reactive component to the voltage. Where the vector is in two dimensional space, the "i" designation is often omitted, but if it were three dimensional space, the vector components would be designated i, j and k.
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