How to find a unit vector u that has the same direction as vector a = 10i + 24j?
Vectors are very important concepts in mathematics, which have many applications in engineering and physics. They are used to calculate the trajectory of an object undergoing projectile motion, as well as the path to be followed by a rocket.
Answer: The unit vector u that has the same direction as vector a = 10i + 24j is u = (5/13)i + (12/13)j
Let's understand the solution in detail.
To calculate the unit vector of a = 10i + 24j, we follow the below steps:
Find the magnitude of the given vector |a| = √(102 + 242) = √676 = 26
Now, we have the formula: a / |a| = u
Using the above formula, we get:
u = (10i + 24j) / 26
u = (5/13)i + (12/13)j