Question

For any two vectors A and B, if $A\cdot B =|A \times B |$ , the magnitude of C = A + B is equal to

• A. $\sqrt{A^2 + B^2}$
• B. $A + B$
• C. $\sqrt{A^2 + B^2 + \frac{AB}{\sqrt2}}$
• D. $\sqrt{A^2 + B^2 + \sqrt2 \, AB}$

Answer 1

The Correct Option is D

AB Cosθ = AB Sinθ

Here, θ = 45°

∣A+B∣ = A2+B2+2ABCos45°

= A2+B2+2AB(1/2)

=A2+B2+2AB

If the vectors are aligned in the same direction then the resulting vector can be obtained by simply adding them. 

Let, A and B are the same-direction vectors, while R is the resulting vector. So, 

R = A + B

The vectors that are aligned in opposite directions are subtracted from each other to produce the resulting vector. Let, vector B is in the opposite direction of vector A. So, the resultant vector R is

R = A - B

If the given vectors are inclined to each other then the resultant vector can be obtained by using the formula below. Here, R is the resultant vector, and A and B are inclined at an angle Θ to each other.

R² = A² + B² + 2ABCos Θ

The resultant value of two or more vectors is calculated using the resultant vector formula depending on the directions of the vectors with regard to one another. The resultant force, also known as the net force, is the total of all the forces acting on a body when two or more forces are present. We use the resultant vector formula to obtain the resultant value of two or more vectors. It is possible to apply the resultant vector formula in mathematics, engineering, and physics.