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

*print*Print*list*Cite

### 2 Answers

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**

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

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

P+Q = 3i-2j+3k.

Therefore |P+Q| = |(3i-2j+3k) = sqrt(3^2+(-2)^2+3^2) = sqrt22.

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

|P-Q| = |-1i+0j-1k| = sqrt((-1)^2 + 0^2+(-1)^2) = sqrt2.