Answer
(a) $E = 3.6$
$F = 2.8$
(b) $E+F = 4.1$
(c) $-E-2F = 6.1$
Work Step by Step
$E = 2\hat{i} + 3\hat{j}$
$F = 2\hat{i} -2 \hat{j}$
(a) We can find the magnitude of the vector E as;
$E = \sqrt{E_x^2+E_y^2}$
$E = \sqrt{(2)^2+(3)^2}$
$E = 3.6$
We can find the magnitude of the vector F as;
$F = \sqrt{F_x^2+F_y^2}$
$F = \sqrt{(2)^2+(-2)^2}$
$F = 2.8$
(b) $E+F = 4\hat{i} + 1\hat{j}$
We can find the magnitude of the vector E+F as;
$E+F = \sqrt{(4)^2+(1)^2}$
$E+F = 4.1$
(c) $-E-2F = -(2\hat{i} + 3\hat{j})-2~(2\hat{i} -2 \hat{j})$
$-E-2F = -6\hat{i} + 1\hat{j}$
We can find the magnitude of the vector -E-2F as;
$-E-2F = \sqrt{(-6)^2+(1)^2}$
$-E-2F = 6.1$
