Question

If$\overrightarrow{\mathbf{V}}\mathbf{=}{\overrightarrow{\mathbf{V}}}_{\mathbf{1}}\mathbf{+}{\overrightarrow{\mathbf{V}}}_{\mathbf{2}}$, is V necessarily greater than$V_1$and/or$V_2$? Discuss.

Short answer

No, V is not greater than $V_1$and $V_2$.

Step-by-step solution

Step 1. Definition of a vector

Any quantity having magnitude and direction is known as a vector. Some examples of vectors are velocity, force, acceleration, momentum, etc.

Step 2. Addition of vectors

The operation of adding two or more vectors is called vector addition. There are two types of vector addition: parallelogram law of vector addition and triangular law of vector addition.

Step 3. Identification of given data

${\overrightarrow{V}}_1$and ${\overrightarrow{V}}_2$are the two vectors having magnitudes $V_1$and $V_2$, respectively. The magnitude of vector $\overrightarrow{V}$is V.

Step 4. Analysis of the vector sum

It is given that $\overrightarrow{V}={\overrightarrow{V}}_1+{\overrightarrow{V}}_2$. The magnitude of the sum of the two vectors, V, is not necessarily greater than the individual magnitudes $V_1$and $V_2$.

For instance, if ${\overrightarrow{V}}_1$and ${\overrightarrow{V}}_2$have the same magnitude but are opposite in direction, then $V=0$. Say, ${\overrightarrow{V}}_1$is a 6 m vector pointing toward the north and ${\overrightarrow{V}}_2$is a 4 m vector pointing toward the south direction, then their sum has a length of 2 m, and is less than either of the two individual vectors.