Question

Exercise 5.1
1.
The vector ā is directed due north and |āl = 24. The vector b is directed due west and b = 7.
Find lā+b|​

Answer 1

Given:

Two vectors

$\vec {a}$ due north and $\vec {b}$ due west.

Magnitude of vector $\vec {a}$ , $|\vec a| = 24$

Magnitude of vector $\vec {b}$ , $|\vec b| = 7$

To find:

$|\vec a+\vec b| = ?$

Solution:

First of all, refer to the attached diagram for the given vectors, their directions and their magnitudes.

These are two perpendicular vectors.

The magnitude of their sum is given as:

$|\vec a+\vec b|=\sqrt{a^2+b^2 }$

Putting the values:

$|\vec a+\vec b|=\sqrt{24^2+7^2 }\\\Rightarrow |\vec a+\vec b|=\sqrt{576+49 }\\\Rightarrow |\vec a+\vec b|=\sqrt{625}\\\Rightarrow |\vec a+\vec b|=\bold{ 25}$

So, the answer is 25.