I know intuitively that the Cross Product of two vectors ##\vec{A}## and ##\vec{B}## represents another vector ##\vec{A \times B}## perpendicular to it. In study of physics we come across this situation a lot. Hence I can visualize some applications of it(adsbygoogle = window.adsbygoogle || []).push({});

I know that the dot product of two vectors ##\vec{A}## and ##\vec{B}## is scalar quantity and also that it represents angular relationship between ##\vec{A}## and ##\vec{B}## .i.e.

- If ##\vec{A}##.##\vec{B} = 0##. Then ##\vec{A}## and ##\vec{B}## are perpendicular.

- If ##\vec{A}##.##\vec{B} > 0## (Positive). Then the angle between ##\vec{A}## and ##\vec{B}## are less than ##90^o##.

- If ##\vec{A}##.##\vec{B} < 0## (Negative). Then the angle between ##\vec{A}## and ##\vec{B}## are greater than ##90^o##.

But I won't be able to understand intuitively, What does the dot product represents. What does the magnitude of the dot product of two vectors represents.

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# Intuitive meaning of Dot Product

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