Question

The dot product of two vectors of magnitudes 3 units and 5units cannot be:

• A. 2
• B. -2
• C. 20
• D. zero

Answer 1

Answer: (C)

20

Dot product of two vectors $\overrightarrow{A}.\overrightarrow{B}=\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|cos\theta$

since $-1\le cos\theta \le 1$

$-\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|\le \overrightarrow{A}.\overrightarrow{B}\le \left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|$

For the given question:

dot product of two vectors of magnitude 3 and 5 units will be:

$-15\le \overrightarrow{A}.\overrightarrow{B}\le 15$

So, dot product cannot be 20 as it is greater than 15.

Hence, option C is correct.