JEE Main
- Exam
- JEE Main
- Subject
- Physics
- Chapter
- Mathematics in Physics
JEE Main · Physics · Mathematics in Physics
An ant starts from the origin and crawls 10 cm~along the x -axis...
An ant starts from the origin and crawls cm~along the -axis and then cm~along the -axis. The dot product of the ant's displacement vector with the position vector of a point that makes ~with the -axis and has a magnitude of & is
Options
- A cm
- B
- C
- D cm
Correct answer
A. cm
Step-by-step solution
Ant's displacement vector& = 10\overset{^}{i} + 20\overset{^}{j} = \overset{→}{a}
Position vector of the given point
~= \sqrt{2}\cos 45 ° \overset{^}{i} + \sqrt{2}\sin 45 ° \overset{^}{j} = \overset{^}{i} + \overset{^}{j} = \overset{→}{b}
Therefore, required dot product will be,~
\overset{→}{a} \cdot \overset{→}{b} = \left(10\overset{^}{i} + 20\overset{^}{j}\right) \cdot \left(\overset{^}{i} + \overset{^}{j}\right) = 10 + 20 = 30cm
