17 - University Physics with Modern Physics

Question

If $\overrightarrow{\mathbf{C}}\mathbf{=}\overrightarrow{\mathbf{A}}\mathbf{+}\overrightarrow{\mathbf{B}}$ , what must be true about the directions and magnitudes of $\overrightarrow{\mathbf{A}}$  and $\overrightarrow{\mathbf{B}}$ if $\mathit{C}\mathbf{=}\mathit{A}\mathbf{+}\mathit{B}$ ? What must be true about the directions and magnitudes of $\overrightarrow{\mathbf{A}}$and $\overrightarrow{\mathbf{B}}$  if $\mathit{C}\mathbf{=}\mathbf{0}$ ?

Step-by-Step Solution

Answer

The magnitude can be any value and direction lie between $\overrightarrow{A}$  and $\overrightarrow{B}$  .

The direction will be opposition and magnitude same.

Vector addition

The addition of two vectors refers to drawing the two vectors on graph paper such that the head of one meet with the rail of the other vector. It is a cumulative addition, i.e., $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{B}+\overrightarrow{A}$ .

Explanation

Part (a)

The magnitude of vector $\overrightarrow{A}$  and $\overrightarrow{B}$  can be any value and direction but the magnitude of  will be in the range of $A+B$  and  $A-B$ and the direction will lies between $\overrightarrow{A}$ and $\overrightarrow{B}$ .

 

Part (b)

 

When the magnitude of vector C is zero, then the direction of vectors A and B will be opposite and the magnitude of A and B will be equal.