The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].
First, we need to determine the value of the vector u by subtracting two vectors whose initial points are at the origin:
[tex]\vec u = (19\,\hat{i} - 8\,\hat{j}) - (21\,\hat{i} + 12\,\hat{j})[/tex]
[tex]\vec u = - 2\,\hat{i} - 20\,\hat{j}[/tex] (1)
According to the statement, vector v is antiparallel to vector u and its magnitude is five times as the magnitude of vector v, which means that (1) must be multiplied by two scalars:
[tex]\vec v = - 1 \,\cdot \, 5\cdot \vec u[/tex] (2)
Please notice that antiparallelism is represented by the scalar - 1, whereas the dilation is represented by the scalar 5.
[tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex]
The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].
The statement presents typing mistakes, correct form is shown below:
Vector u has initial points at (21, 12) and its terminal point at (19, - 8). Vector v has a direction opposite that of u, whose magnitud is five times the magnitud of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?
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