SOLUTION: Please help me with this vectors problem:
Given vectors of magnitude 3 and 4 with an angle between them of 80°, find the magnitude of the resultant.
Enter answer accurate to t
Question 979889: Please help me with this vectors problem:
Given vectors of magnitude 3 and 4 with an angle between them of 80°, find the magnitude of the resultant.
Enter answer accurate to two decimal places.
Thank you in advanced. Found 2 solutions by Alan3354, ikleyn:Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Given vectors of magnitude 3 and 4 with an angle between them of 80°, find the magnitude of the resultant.
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Place the start of one vector at the end of the first.
The resultant is the 3rd side of the triangle.
The interior angle = 100 degs
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Use the Cosine Law:
r^2 = 3^2 + 4^2 - 2*3*4*cos(100)
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
Resultant is the sum of given vectors, correct?
The sum of vectors is the diagonal of a parallelogram built on these vectors. Do you know it? See the Figure below.
Figure. The sum of the vectors AB + AD = AC (the parallelogram rule)
So, we are given the vectors AB and AD of the length 3 and 4 and the angle LA = 80° between them.
The magnitude of the resultant is the length of the vector of sum, which is the vector AC.
Apply the Law of Cosines (see the lesson Proof of the Law of Cosines revisited in this site) to the triangle ADC to find the measure of its side AC.