Question

The components of vector A are Ax = +2.2 and Ay = -6.9 , and the components of vector B are given are Bx =

-6.1 and By = -2.2. What is the magnitude of the vector B - A

Answer 1

For simplicity, let's call vector B-A vector C Then C is
Cx = (-6.1 - 2.2)
Cy = (-2.2 - (-6.9)) Or,
Cx = -8.3 Cy = 4.7
The magnitude is found with the Pythagorean theorem
||C|| = √(-8.3² + 4.7²) = 9.538

Answer 2

`|\vec B - \vec A| = 9.54`

Step-by-step explanation:

As we know that

`A_x = 2.2 \: A_y = -6.9`

so we have

`\vec A = 2.2 \hat i - 6.9 \hat j`

Also we know that

`B_x = -6.1 \: B_y = -2.2`

so we will have

`\vec B = -6.1 \hat i - 2.2 \hat j`

now we need to find magnitude of B - A

so we have

`\vec B - \vec A = (-6.1 \hat i - 2.2 \hat i) + (-2.2\hat j + 6.9 \hat j)`

`\vec B - \vec A = -8.3 \hat i + 4.7 \hat j`

magnitude of this vector is given as

`|\vec B - \vec A| = √(8.3^2 + 4.7^2)`

`|\vec B - \vec A| = 9.54`