Question

Consider the three dip1acement vectors A = (3i - 3j) m, B = (i-4j) m, and C = (-2i + 5j) m. Use the component method to determine:

(a) the magnitude and direction of the vector D=A+B+C and
(b) the magnitude and direction of E=-A - B + C.

Answer 1

(a)
`\vec D = 2\,i - 2\,j`, (b)
`\vec E = -6\,i + 12\,j`

Step-by-step explanation:

Let be
`\vec A = 3\,i - 3\,j\,[m]`,
`\vec B = i - 4\,j\,[m]` and
`\vec C = -2\,i + 5\,j \,[m]`, each resultant is found by using the component method:

(a)
`\vec D = \vec A + \vec B + \vec C`

`\vec D = (3\,i - 3\,j) + (i-4\,j) + (-2\,i+5\,j)\,[m]`

`\vec D = (3\,i + i -2\,i)+(-3\,j-4\,j+5\,j)\,[m]`

`\vec D = (3 + 1 -2)\,i + (-3-4+5)\,j\,[m]`

`\vec D = 2\,i - 2\,j`

(b)
`\vec E = -\vec A - \vec B + \vec C`

`\vec E = -(3\,i-3\,j)-(i - 4\,j)+(-2\,i+5\,j)`

`\vec E = (-3\,i + 3\,j) +(-i+4\,j) + (-2\,i + 5\,j)`

`\vec E = (-3\,i-i-2\,i) + (3\,j+4\,j+5\,j)`

`\vec E = (-3-1-2)\,i + (3+4+5)\,j`

`\vec E = -6\,i + 12\,j`