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Write any five properties of vector product of two vectors. |
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Answer» Solution :(i) The vector product of any two vectors is always another vector whose direction is perpendicular to the plane containing these two vectors, i.e., orthogonal to both the vectors `vecA` and `vecB`, even though the vectors `vecA` and `vecB` may or may not be mutually orthogonal. (ii) The vector product of two vectors is not commutative, i.e., `vecA xx vecB ne vecB xx vecA`. But, `vecA xx vecB = - vecB xx vecA`. Here it is worthwhile to note that `|vecA xx vecB| = |vecB xx vecA|` = AB sin `theta` i.e., in the case of the product vectors `vecA xx vecB` and `vecB xx vecA`, the magnitudes are equal but directions are opposite to each other. (III) The vector product of two vectors will have maximum magnitude when sin `theta` = 1, i.e., `theta = 90^(@)` i.e., when the vectors `vecA` and `vecB` are orthogonal to each other. `(vecA xx vecB)_(max)` = AB n (iv) The vector product of two non-zero vectors will be minimum when sin `theta` = 0, i.e., `theta = 0^(@)` or `180^(@)` `(vecA xx vecB)_(min)` = 0 i.e., the vector product of two non-zero vectors VANISHES, if the vectors are either parallel or antiparallel. (v) The self-cross product, i.e., product of a vector with itself is the null vector `vecA xx vecA` = AA sin `0^(@)` n = `VEC0` In physics the null vector `vec0` is simply denoted as zero. |
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