Question

Two vectors of equal magnitude 5 unit have an angle
60° between them. Find the magnitude of (a) the sum of
the vectors and (b) the difference of the vectors.



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Answer 1

Answer:

Sum of vectors is 5$\sqrt{3}$ and difference of vectors is 5.

Explanation:

Let the vectors be a and b.  

|a + b|² = (a + b). (a + b)  

= |a|² + |b|² + 2a.b (noting that a.b = b.a))  

= 25 + 25 +2 x 5 x 5 cos60°  

= 50 +50 x (1/2) = 75.  

So |a + b| = $\sqrt{75}$=5√3

|a - b|² = (a - b). (a - b)  

= |a|² + |b|² - 2a.b (noting that a.b = b.a))  

= 25 + 25 - 2 x 5 x 5 cos60°  

= 50 - 50 x (1/2) = 25.  

So |a - b| = 5.

Sum of vectors is 5$\sqrt{3}$ and difference of vectors is 5.

I have attached the pictures of Vectors.