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FromTheMoon [43]
3 years ago
10

Calculate a vector c in the same direction of the vector a and that has the same length as the vector b

Mathematics
1 answer:
Viktor [21]3 years ago
8 0

For any scalar t>0, t\vec a is a vector pointing in the same direction as a.

To force this vector to have the same length as another vector \vec b, first normalize t\vec a by dividing it by its norm,

\dfrac{t\vec a}{\|t\vec a\|}=\dfrac{t\vec a}{t\|\vec a\|}=\dfrac{\vec a}{\|\vec a\|}

then multiply this vector by the norm of \vec b, so that

\vec c=\dfrac{\|\vec b\|}{\|\vec a\|}\vec a

To confirm that \vec c has the same length as \vec b:

\|\vec c\|=\left\|\dfrac{\|\vec b\|}{\|\vec a\|}\vec a\right\|=\dfrac{\|\vec b\|}{\|\vec a\|}\|\vec a\|=\|\vec b\|

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The answers to this questions would be:

1. A-> (1.5, 1.5)                              5. A and B->  7 units  

2. B-> (-2, -1.5)                               6. C and D->  3 units  

3. C-> (-3.5, 2)                                7. B and D-> 1 unit

4. D-> (0.5, 0)                                 8. A and D-> 8 units

-------------------------------- WORD PROBLEMS------------------------------------------

9. 8 feet

10a. (-4, -1)                                              10b. (4, 1)


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Answer:

hi

Step-by-step explanation:

Sorry u gonna fail cause I to dumb.

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