Let A = 4i - 2j, B = -3i + 5j, and E = 2A + 3B. What are the magnitude and direction of vector E?

Let A = 4i - 2j, B = -3i + 5j, and C = A + B. What are the magnitude and direction of vector C?

Four forces are exerted on the object shown in FIGURE $P3.45$. (Forces are measured in newtons, abbreviated $\text{N}$.) The net force on the object is ${\vec{F}}_{\text{net}}={\vec{F}}_1+{\vec{F}}_2+{\vec{F}}_3+{\vec{F}}_4=4.0\hat{i}\text{N}$. What are (a) ${\vec{F}}_3$ and (b) ${\vec{F}}_4$? Give your answers in component form.

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. What are the magnitude and direction of vector F?

(II) For the vectors shown in Fig. 3–41, determine

(b) 2 A (→ above A) ― 3 B (→ above B) + 2 C (→ above C) , and

(II) Three vectors are shown in Fig. 3–41. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the +𝓍 axis.

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Figure 3–39 shows two vectors, $\overrightarrow{A}$ and $\overrightarrow{B}$, whose magnitudes are A = 6.8 units and B = 5.5 units. Determine $\overrightarrow{C}$ if $\overrightarrow{C}$ = $\overrightarrow{A}$ + $\overrightarrow{B}$. Give the magnitude and direction for each.

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. Draw a coordinate system and on it show vectors A, B, and F.