Question

The vector ab has a magnitude of 20 units and is parallel to the vector 4i + 3j. find ab.

Answer 1

The vector ab has a magnitude of 20 units and is parallel to the

vector 4i + 3j. Hence, The vector AB is 16i + 12j.

How to find the vector?

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

Given;

The vector ab has a magnitude of 20 units and is parallel to the

vector 4i + 3j.

magnitude

$\sqrt{4^2 + 3^2} \\\\\sqrt{16 + 9} \\\\= 5$

Unit vector in direction of resultant = (4i + 3j) / 5

Vector of magnitude 20 unit in direction of the resultant

= 20  x (4i + 3j) / 5

= 4 x (4i + 3j)

= 16i + 12j

Hence, The vector AB is 16i + 12j.

Learn more about vectors;

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