Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
In this lesson, we will learn how to find the angle between two vectors in space using their dot product.
Q1:
If , , and , where is a unit vector, find the measure of the angle between and rounded to the nearest minute given .
Q2:
Find the angle π between the vectors V = β¨ 5 , 1 , β 2 β© and W = β¨ 4 , β 4 , 3 β© . Give your answer correct to two decimal places.
Q3:
The angle between A and B is 2 2 β . If | | = 3 | | = 2 5 . 2 A B , find A B β to the nearest hundredth.
Q4:
Find .
Q5:
Find the angle between the vectors and . Give your answer correct to two decimal places.
Q6:
Find the angle π between the vectors V = β¨ 2 , 1 , 4 β© and W = β¨ 1 , β 2 , 0 β© .
Q7:
Given that , , and , determine the size of the smaller angle between the two vectors.
Q8:
Given that and , determine, to the nearest hundredth, the size of the smaller angle between the two vectors.
Q9:
Q10:
Given , , , and , determine the size of the angle between vectors and approximated to the nearest hundredth.
Q11:
Q12:
Q13:
If and , find the size of the angle between the two vectors approximated to the nearest hundredth.
Q14:
Q15:
Find the angle π between the vectors V = β¨ 4 , 2 , β 1 β© and W = β¨ 8 , 4 , β 2 β© .
Q16:
Find the value of π₯ given A = ο± 4 π , π₯ , π ο΅ c o s l o g s i n 3 , B = ο± π , 1 6 , 4 π ο΅ c o s l o g s i n 2 and A B β = 1 0 where π is the angle between the vectors A and B . Give the answer to two decimal places.
Q17:
Find the angle π between the vectors V i j k = β + 2 + and W i j k = β 3 + 6 + 3 .
Q18:
Find the angle π between the vectors V = β¨ 7 , 2 , β 1 0 β© and W = β¨ 2 , 6 , 4 β© . Give your answer correct to one decimal place.
Donβt have an account? Sign Up
