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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

Respuesta :

egenriether
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:

[tex]|\vec B - \vec A| = 9.54[/tex]

Explanation:

As we know that

[tex]A_x = 2.2 \: A_y = -6.9[/tex]

so we have

[tex]\vec A = 2.2 \hat i - 6.9 \hat j[/tex]

Also we know that

[tex]B_x = -6.1 \: B_y = -2.2[/tex]

so we will have

[tex]\vec B = -6.1 \hat i - 2.2 \hat j[/tex]

now we need to find magnitude of B - A

so we have

[tex]\vec B - \vec A = (-6.1 \hat i - 2.2 \hat i) + (-2.2\hat j + 6.9 \hat j)[/tex]

[tex]\vec B - \vec A = -8.3 \hat i + 4.7 \hat j[/tex]

magnitude of this vector is given as

[tex]|\vec B - \vec A| = \sqrt{8.3^2 + 4.7^2}[/tex]

[tex]|\vec B - \vec A| = 9.54[/tex]

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