Question

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problem 2: vector v has initial point (4, 3) and terminal point (-7, 9). write v as a linear combination of the standard unit vectors i and j.

v =

Explanation:

Step1: Find the component form of the vector

To find the component form of a vector with initial point \((x_1, y_1)\) and terminal point \((x_2, y_2)\), we use the formula \(\mathbf{v}=\langle x_2 - x_1, y_2 - y_1
angle\). Here, \(x_1 = 4\), \(y_1 = 3\), \(x_2=-7\), and \(y_2 = 9\). So, \(x_2 - x_1=-7 - 4=-11\) and \(y_2 - y_1=9 - 3 = 6\). Thus, the component form of \(\mathbf{v}\) is \(\langle - 11,6
angle\).

Step2: Write as a linear combination of \(\mathbf{i}\) and \(\mathbf{j}\)

The standard unit vectors \(\mathbf{i}=\langle1,0
angle\) and \(\mathbf{j}=\langle0,1
angle\). A vector \(\langle a,b
angle\) can be written as \(a\mathbf{i}+b\mathbf{j}\). So, \(\langle - 11,6
angle=-11\mathbf{i}+6\mathbf{j}\).

Answer:

\(-11\mathbf{i} + 6\mathbf{j}\)