Question

vector a is 4 units left. vector b is 9 units up. what is the magnitude (the length) of the addition of vector a + vector b?

Explanation:

Step1: Represent vectors in coordinate system

Vector A is 4 units left, so in x - direction, \( \vec{A}=(- 4,0) \). Vector B is 9 units up, so in y - direction, \( \vec{B}=(0,9) \). The resultant vector \( \vec{R}=\vec{A}+\vec{B}=(-4 + 0,0 + 9)=(-4,9) \)

Step2: Use magnitude formula for vector \((x,y)\)

The magnitude of a vector \( \vec{R}=(x,y) \) is given by \( |\vec{R}|=\sqrt{x^{2}+y^{2}} \). Here \( x=-4 \), \( y = 9 \), so \( |\vec{R}|=\sqrt{(-4)^{2}+9^{2}}=\sqrt{16 + 81}=\sqrt{97}\approx9.85 \)

Answer:

The magnitude of \( \vec{A}+\vec{B} \) is \( \sqrt{97}\approx9.85 \) units.