This post categorized under Vector and posted on October 13th, 2019.

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Given three vectors we can define their double cross or double vector product a (b c) and their mixed double product the dot product of one with the vector product of the other two a (b c). Both of these double products are linear in each of the three factors a b and c. properties of the double cross a (b c) 1. It is a vector. 2. If the vectors are expressed in terms of unit vectors i j and k along the x y and z directions the scalar product can also be expressed in the form The scalar product is also called the inner product or the dot product in some mathematics texts. b 3)j (a 1 b 2 a 2 b 1)k . Cross Product Note the result is a vector and NOT a scalar value. For this reason it is also called the vector product. To make this definition easer to remember we usually use determinants to calculate the cross product. Determinants Determinant of order 2 Determinant of order 3 Cross Product We can now rewrite the definition for the cross product

Upload failed. Please upload a file larger than 100x100 pixels We are experiencing some problems please try again. You can only upload files of type PNG JPG or JPEG. Saclar projection1sqrt3 and Vector projection 13(hatihatjhatk) We have been given two vectors veca and vec b we are to find out the scalar and vector projection of vec b onto vec a we have vecahatihatjhatk and vecbhati-hatjhatk The scalar projection of vec b onto vec a means the theta 76.5o Were asked to find the angle between two vectors given their unit vector notations. To do this we can use the equation vecA vecB ABcostheta rearranging to solve for angle theta costheta (vecA vecB)(AB) theta arccos((vecA vecB)(AB)) where vecA vecB is the dot product of the two vectors which is vecA

Answer to Find the scalar products ii jj and kk The vector product mc-TY-vectorprod-2009-1 One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result as the name suggests is a vector. So by the above relationships the unit basis vectors i j and k of an orthonormal right-handed (Cartesian) coordinate frame must all be pseudovectors (if a basis of mixed vector types is disallowed as it normally is) since i j k j k i and k i j. Because the cross product may also be a (true) vector it may not change