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Motion In A Plane

Question
CBSEENPH11018346

What are the characteristics of cross product?

Solution
Characteristics of cross product are:
(i) Cross product of two vectors is anti commutative.
That is, 
                         space straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space minus straight B with rightwards arrow on top cross times straight A with rightwards arrow on top
(ii) Cross product is distributive,
That is, 
 
                 space straight A with rightwards arrow on top cross times left parenthesis straight B with rightwards arrow on top plus stack straight C right parenthesis with rightwards arrow on top space equals space straight A with rightwards arrow on top cross times straight B with rightwards arrow on top plus straight A with rightwards arrow on top cross times straight C with rightwards arrow on top
(iii)Cross product of two parallel vectors is zero.
That is, 
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(iv) Cross product of two vectors is equal to the area of parallelogram formed by two vectors.
(v) Area of triangle formed by two vectors and their resultant is equal to half the magnitude of cross product.