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
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(374 Votes)
Tristan
Professional · Tutor for 6 years
Answer
Thus, A part follows the formula and curriculum on solving 3 times a multiple which says
,means vector f is three times of vector e.For part B,
as a column vector will be 3 times the column vector of
. If we represent
as a columns vector such as
where
and
are the components of
, then
will be:
They are the terms of
as columnBibleke. Thus, the problem is resolved successfully!
Explanation
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*vecfb) 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: