Vector f is parallel to vector e, in the same direction and 3 times as long. a) Write f in terms of e b) Write f as a column vector.

Question

Question

Vector f is parallel to vector e, in the same direction and 3 times as long. a) Write f in terms of e b) Write f as a column vector.

Answer 1

Thus, A part follows the formula and curriculum on solving 3 times a multiple which says \[ \boldsymbol{f} = 3 \cdot \boldsymbol{e} \], means vector f is three times of vector e. For part B, \(\boldsymbol{f}\) as a column vector will be 3 times the column vector of \(\boldsymbol{e}\). If we represent \(\boldsymbol{e}\) as a columns vector such as \[ \boldsymbol{e}= \begin{bmatrix} e1 \\ e2 \\ en \end{bmatrix} \] where \(e1, e2,\) and \(en\) are the components of \(e\), then \(f\) will be: \[ \boldsymbol{f}= 3 \cdot \begin{bmatrix} e1 \\ e2 \\ en \end{bmatrix}= \begin{bmatrix} 3e1 \\ 3e2 \\ 3en \end{bmatrix} \] They are the terms of \(f\) as columnBibleke. Thus, the problem is resolved successfully!

Answer 2

This question also involves the mathematical concept of vectors and involves a simpler procedure than the previous one to determine a vector parallel to a given vector and also a variable times the length of the initial given vector. The solution will be easier as compared to previous questions. Based on our knowledge of vectors, a steady concept is, that if two vectors are parallel to each other, they are a constant multiple of one another. a) For the first part, since vector f is parallel to vector e, the same direction and three times as long, then Geometrically speaking f is simply a multiplication of e by 3, such that vecf = 3*vecf b) For the second part, given that the vectors are parallel and 3 times as long as e, we presume we have converted vector e into a column as [e1, e2,...en ]'. If we want to make vector f three times as long as this column vector without changing its direction, we simply need to multiply each of these n components of e column construct by 3, and that's pretty much it, so as a column vector ‘f’ would be expected to be drafted [3e1, 3e2,...3en ]' . Now let's move on towards putting things together through iterations:

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Vector f is parallel to vector e, in the same direction and 3 times as long. a) Write f in terms of e b) Write f as a column vector.

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