Given the forces P=i-j+k and Q=2i-j+2k determine the magnitude of P+Q, P-Q.

We'll calculate the magnitude of a force with the
formula:

|F| = sqrt(a^2 + b^2 + c^2), where F = ai + bj +
ck

In order to add 2 vectors, P and Q, we'll add or
subtract algebraically the coefficients of correspondent unit vectors:
i,j,k.

P = i - j + k

Q = 2i -
j + 2k

P + Q = (1+2)i + (-1-1)j +
(1+2)k

P + Q = 3i - 2j +
3k

The magnitude of the resultant of the addition of P and
Q is:

|P + Q| = sqrt[3^2 + (-2)^2 +
(3)^2]

|P + Q| = sqrt(9 + 4 +
9)

|P + Q| = sqrt
22

We'll calculate the resultant of
P-Q:

P-Q = (1-2)i + (-1+1)j +
(1-2)k

P-Q = -i + 0j - k

The
magnitude of the resultant of P-Q is:

|P - Q| = sqrt[(-1)^2
+ (0)^2 + (-1)^2]

|P - Q| =
sqrt(1+1)

|P - Q| = sqrt
2