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Explain the kinds of multiplication operations for vectors . |
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Answer» Solution :There are TWO kind of multiplication of VECTORS : (i) If the product of two vector quantities results into a scalar then the product called a scalar product . This product is also known as DOT product . The scalar products of two vectors `vec(A) and vec(B)`is DENOTED by `vec(A ) . vec(B ) = | vec(A) | |vec(B)|` where A and B are the magnitudes of `|vec (A)|and |vec (B)|` respectively and `theta`is the angle between `vec(A) and vec(B)` (ii) Vector product [Corss product ] : If the product of two vector quantities results into a vector then the product is called a vector product . A vector product is represente d by keeping cross sign `(xx)` between two vectorshence it is also called cross product of vectors . Suppose `theta ` is the angle between `vec(A) and vec(B)`then its vector product is , `vec(A).vec(B ) = |vec(A) ||vec(B)|sin theta hat (n)` `= AB sin theta hat(n)` where `hat(n)`is the unit vector in the direction perpendicular to the plane formed by `hat(A) and hat(B)` and B are the MAGNITUDE of `hat(A) and hat(B)` respectively . |
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