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andriy [413]
1 year ago
12

Let the vector v v have an initial point at ( 1 , − 7 ) (1,−7) and a terminal point at ( 3 , − 2 ) (3,−2). Determine the compone

nts of vector v . v.
Mathematics
1 answer:
Yuliya22 [10]1 year ago
3 0

Answer:  The vector is < 2, 5 >

==========================================================

Explanation:

Label the initial point (1,-7) as point P and (3,-2) as point Q.

  • The x coordinate of P is 1
  • The x coordinate of Q is 3

This is a change of +2, meaning we move 2 units to the right.

Therefore, the x component of the vector is +2 or simply 2.

  • The y coordinate of P is -7
  • The y coordinate of Q is -2

This is a change of +5 when moving from P to Q. We have moved 5 units up. The y coordinate of the vector is +5 or simply 5.

Overall, the vector is < 2, 5 > which tells the reader "move 2 units to the right and 5 units up.

Refer to the diagram below.

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5

Step-by-step explanation:

Refer to attachment for marking of sides.

In the given figure , ∆ABC , ∆ABD and ∆ADC are right angled triangles . Therefore here we can use the Pythagoras theorem , as ,

\longrightarrow base² + perpendicular² = hypotenuse ² .

<u>•</u><u> </u><u>In </u><u>∆</u><u>A</u><u>B</u><u>D</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>;</u>

\longrightarrow AB² + BD² = AD²

\longrightarrow AB² + x² = 10²

\longrightarrow AB² = 10² - x²

\longrightarrow AB² = 100 - x²

\rule{200}2

<u>•</u><u> </u><u>Again</u><u> </u><u>in </u><u>∆</u><u>A</u><u>D</u><u>C</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>;</u>

\longrightarrow AC² + AD² = CD²

\longrightarrow AC² = 20² - 10²

\longrightarrow AC² = 400 - 100

\longrightarrow AC² = 300

\rule{200}2

<u>Again</u><u> </u><u>in </u><u>∆</u><u>A</u><u>B</u><u>C</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>,</u>

\longrightarrow AC² = AB² + BC²

Substituting the values from above ,

\longrightarrow 300 = 100-x² + (20-x)²

\longrightarrow 300 = 100 - x² + 400 + x² - 40x

\longrightarrow 40x = 500 - 300

\longrightarrow 40x = 200

\longrightarrow x = 200/40

\longrightarrow x = 5

<h3>Hence the required answer is 5 .</h3>

8 0
2 years ago
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