Define a vector. Give examples.

Write a short note on the scalar product between two vectors.

The position vectors particle has length 1m and makes 30° with the x-axis. What are the lengths of the x and y components of the position vector?

Calculate the average velocity of the particle whose position vector changes from \(\overrightarrow { { r }_{ 1 } } =5\hat { i } +6\hat { j } \) to \(\overrightarrow { { r }_{ 2 } } =2\hat { i } +3\hat { j } \)  in a time 5 second.

What are the resultants of the vector product of two given vectors given by \(\overrightarrow { A } =4\hat { i } -2\hat { j } +\hat { k } \ and \ \overrightarrow { B } =5\hat { i } +3\hat { j } -4\hat { k } \)