Vector u has its initial point at (15, 22) and its terminal point at (5, -4). Vector v points in a direction opposite that of u,
and its magnitude is twice the magnitude of u. What is the component form of v?
1 answer:
Though the vectors are going in opposite directions, their terminal and starting points are the same, just switched, check the picture below.
recall the component for (a,b), (c,d) is just (c-a , d-b),
the component form for "v" is then
(5, -4), (15, 22) => (15 - 5, 22-(-4)) => (15 - 5, 22+4) => (10 , 26).
and since "v" is twice as long as "u", then its form is 2v, or
2(10 , 26) => (20, 52)
recall the component for (a,b), (c,d) is just (c-a , d-b),
the component form for "v" is then
(5, -4), (15, 22) => (15 - 5, 22-(-4)) => (15 - 5, 22+4) => (10 , 26).
and since "v" is twice as long as "u", then its form is 2v, or
2(10 , 26) => (20, 52)
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Answer: Choice B
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Explanation:
The given matrix is
The numbers to the right of the vertical bar represent the values on the right hand side of each equation in the final answer.
The numbers to the left of the bar represent the x and y coefficients of the equations. The first number of any given row is the x coefficient. The second number is the y coefficient.
For instance, the first row has to indicate the x coefficient is 1, and the y coefficient is 5. We end up with 1x+5y or simply x+5y. Putting everything together, the first equation would be x+5y = 11
Through similar steps, the second equation is 4x-6y = -3