Question

Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by a2 + b2 > c2. Which one of the following statements concerning these vectors is true?

The angle between the two vectors must be an obtuse angle, i.e, greater than 90 The two vectors must point in opposite directions
The two vectors must point in opposite directions
The two vectors must be parallel.
The angle between the two vectors must be an acute angle, l-e, less than 900.

Answer 1

D.The angle between the two vectors must be an acute angle which is less than 90 degrees.

Explanation:

We are given that two vectors A and B are added together to form a vector C.

The relationship between the magnitudes of the vectors is given by
`a^2+b^2 >c^2`

We have to find which statement is true about given vectors.

We know that if a triangle is an obtuse triangle then

`c^2 >a^2+b^2`

If a triangle is an acute triangle then

`a^2+b^2 >c^2`

If a triangle is right angle triangle then

`c^2=a^2+b^2`

Therefore,the angle between the two vectors must be an acute angle which is less than 90 degrees.

Option D is true.