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

Answer:

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

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) $\vec E = -\vec A - \vec B + \vec C$

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

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

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

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

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