Respuesta :

luisejr77

Answer:

Third Option

[tex]B = -0.5A[/tex]

Explanation:

If we have a vector A = ax + by we know that by definition

cA = cax + cby

Where c is a constant.

In this case we have two vectors

[tex]A = 7.6\^x -9.2\^y\\\\B = -3.8\^x + 4.6\^y[/tex]

You may notice that vector B has an opposite direction to vector A.

You may also notice that | Ax | is the double of | Bx | and | Ay | is double of |By |

That is to say

[tex]3.8 +3.8 = 7.6\\\\4.6 +4.6 = 9.2[/tex]

So the equation that relates to vectors A and B is:

[tex]B = -0.5A[/tex].

You can verify this relationship by performing the operation

[tex]B = -0.5A[/tex]

[tex]-3.8\^x + 4.6\^y = -0.5(7.6\^x -9.2\^y)\\\\\-3.8\^x + 4.6\^y = -3.8\^x + 4.6\^y[/tex]

mixter17

Hello!

The answer is:

The third option,

[tex]B=-0.5A[/tex]

Why?

To solve the problem, we need to remember the following vector property:

Vector multiplied by a scalar or constant number:

Multiplying a vector by a scalar number results in multiplying each of the components of the vector (x, y and z) by the scalar or constant number (including its sign).

So, we are given the following vectors:

[tex]A=(7.6,-9,2)\\B=(-3.8,4.6)[/tex]

So, writing an equation that involves both given vectors, we have:

[tex]B=-0.5A\\\\(-3.8,4.6)=-0.5((7.6,-9,2))=((-0.5*7.6),(-0.5*-9.2)\\\\(-3.8,4.6)=(-3.8,4.6)[/tex]

Hence, we have that the answer is the third option,

[tex]B=0.5A[/tex]

Have a nice day!

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