Question

Can someone help me?!!!!!

Answer 1

Hello!

The answer is:

The third option,

`B=-0.5A`

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:

`A=(7.6,-9,2)\\B=(-3.8,4.6)`

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

`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)`

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

`B=0.5A`

Have a nice day!

Answer 2

Third Option

`B = -0.5A`

Step-by-step 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

`A = 7.6\^x -9.2\^y\\\\B = -3.8\^x + 4.6\^y`

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

`3.8 +3.8 = 7.6\\\\4.6 +4.6 = 9.2`

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

`B = -0.5A`.

You can verify this relationship by performing the operation

`B = -0.5A`

`-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`