Question

Which of the following vector indentities is false?

• A. $\overrightarrow{P}\to +\overrightarrow{Q}\to =\overrightarrow{Q}\to +\overrightarrow{P}\to$
• B. $\overrightarrow{P}\to +\overrightarrow{Q}\to =\overrightarrow{Q}\to \times \overrightarrow{P}\to$
• C. $\overrightarrow{P}\to .\overrightarrow{Q}\to =\overrightarrow{Q}\to .\overrightarrow{P}\to$
• D. $\overrightarrow{P}\to \times \overrightarrow{Q}\to \ne \overrightarrow{Q}\to \times \overrightarrow{P}\to$

Answer 1

The correct option is B $\overrightarrow{P}\to +\overrightarrow{Q}\to =\overrightarrow{Q}\to \times \overrightarrow{P}\to$

Vector Properties

1. Commutative Property of Addition- For any two vectors a and b, $\Rightarrow \overline{a}+\overline{b}=\overline{b}+\overline{a}$,

2. Associative Property of addition - For any three vectors $\overline{a}$, $\overline{b}$ and $\overline{c}$, $\Rightarrow (\overline{a}+\overline{b})+\overline{c}=\overline{a}+(\overline{b}+\overline{c})$

3. Additive Identity- For any vector $\overline{a}$, $\Rightarrow \overline{a}+0=0+\overline{a}=\overline{a}$

4. Distributivity of scalar product over addition- Let $a$, $\overline{b}$ and $\overline{c}$ be any three vectors, then $\Rightarrow \overline{a}.(\overline{b}+\overline{c})=\overline{a}.\overline{b}+\overline{a}.\overline{c}$

5. Commutative Property of scalar product- For any two vectors a and b, $\Rightarrow \overline{a}.\overline{b}=\overline{b}.\overline{a}$,

6. Vector product is not commutative- For any two vector $\overline{a}$ and $\overline{b}$ $\Rightarrow \overline{a}\times \overline{b}=-\overline{b}\times \overline{a}$ $\Rightarrow \overline{a}\times \overline{b}\ne \overline{b}\times \overline{a}$