Question

Vector a+b+c = 0 magnitude of |a| = 3 |b|= 4 and |c| = 15 .find the angle between a and b.

Answer 1

Answer:

90°

Step-by-step explanation:

Perhaps it should say |c|=5.  Because it is impossible that |c|=15.  Actually, the triangle inequality gives:

       |c| = |-c| = |a+b| ≤ |a| + |b| = 3 + 4 = 7

So let's use |c| = 5.

Method 1

Since the lengths of the sides are 3, 4, 5, we have a right angled triangle with hypotenuse c.  The angle between a and b is then 90°.

Method 2

a + b + c = 0

=> a + b = -c

=> ( a + b ) · ( a + b ) = ( -c ) · ( -c )

=> a·a + b·b + 2a·b = c·c

=> |a|² + |b|² + 2a·b = |c|²

=> 9 + 16 + 2a·b = 25

=> a·b = 0

=> a and b are orthogonal  ( since a≠0 and b≠0 )

So the angle between a and b is 90°