What should be the angle theta between two vectors A and B for their resultant R to be maximum?

Question

Answer

Angle between two vectors for maximum resultant

When two vectors are added, the resultant vector is obtained. The magnitude of the resultant vector is maximum when the two vectors are in the same direction. In the case of two vectors A and B, their resultant R is given by:

R = A + B

where A and B are the magnitudes of vectors A and B, respectively. The angle between the two vectors is given by theta (θ).

Explanation

The magnitude of the resultant vector can be expressed as:

|R| = √(A² + B² + 2AB cosθ)

To find the angle theta that gives the maximum value of R, we need to differentiate the above equation with respect to theta and equate it to zero:

d|R|/dθ = -2AB sinθ = 0

This implies that sinθ = 0, which means that θ = 0 or θ = π. Therefore, the angle between the two vectors should be either 0 degrees or 180 degrees for the resultant vector to be maximum.

Conclusion

The angle between two vectors A and B for their resultant R to be maximum is either 0 degrees or 180 degrees. In other words, the two vectors should be either in the same direction or in opposite directions. When the two vectors are perpendicular to each other, their resultant vector is minimum.

Answer

when cos theta would be max .i.e. 1 so theta will be 0 degree

Similar Class 12 Doubts

A vector and b vector are two vectors of equal magnitude and theta is the angle between them. The angle between a vector or b vector with their resultant is?

If two vectors a&b are such that |a.b|=|a×b|,then find the angle between the vectors a&b?

if a and b are unit vectors such that 2a-4b and 10a 8b are perpendicular to each other ,find the angle between the vectors a and b ?

a and b are 2 unit vectors then what is the angle between a and b if root 3 a minus b is also a unit vector

How to find angle between resultant electric field and radial field?

Top Courses for Class 12

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams