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Thought-Process to Discover Knowledge

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mathsVector AlgebraProperties of Dot Product

### Distributive Property over Vector Addition

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What does 'distributive' mean?

• to restrict; to arrest

Given the definition of dot product as
vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z
What is vec p cdot (vec q+vec r)

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

The answer is 'all the above'.

•  Dot product of sum of vectors is sum of dot products with the vectors - Distributive.

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

Solved Exercise Problem:

If the dot products of two vectors vec a and vec b with a third vector vec c are 2 and 3, what is vec c cdot (vec a + vec b) ?

• 5
• 5
• 6
• 2/3
• 3/2

Answer is '5'.

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