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Thought-Process to Discover Knowledge

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mathsProperties of Vector ArithmeticsProperties of Cross Product

### Distributive Property over Vector Addition

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What does 'distributive' mean?

• to restrict; to arrest

Given the definition of cross product as
vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|
What is vec p xx (vec q+vec r)

• vec p xx ((q_x+r_x)i+(q_y+r_y)j+(q_z+r_z)k)
• |(i, j, k),(p_x, p_y, p_z),(q_x+r_x, q_y+r_y, q_z+r_z)|
• vec p xx vec q + vec p xx vec r
• all the above
• all the above

The answer is 'all the above'.

•  Cross product of sum of vectors is sum of cross products with the vectors - Distributive.

Distributive Property: For any given vectors vec p, vec q, vec r in bbb V
vec p xx (vec q + vec r) = vec p xx vec q + vec p xx vec r

Solved Exercise Problem:

If the cross products of vec c with two vectors vec a and vec b are 2 and 3, what is vec c xx (vec a + vec b) ?

• 5
• 5
• 6
• 2/3
• 3/2

Answer is '5'.

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