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mathsVector AlgebraProperties of Cross Product

### cross product of a negative

In this page, you will learn about the vector cross product with the negative of a vector.

click on the content to continue..

Given vec p = 2i+j-k what is the negative of vec p?

• 2i+j-k
• -2i-j+k
• -2i-j+k

The answer is '-2i-j+k'

Given the definition of cross product as
vec p xx vec q = |vec p||vec q|sin theta hat n
What is vec p xx (-vec q)?

• -(vec p xx vec q)
• |p||q|sin(180+theta) hat n
• -|p||q|sin(theta) hat n
• all the above
• all the above

The answer is 'All the above'

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 p xx vec q)
• |(i, j, k),(p_x, p_y, p_z),(-q_x, -q_y, -q_z)|
• -|(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|
• all the above
• all the above

The answer is 'All the above'

•  Cross product with a negative of a vector is the negative of cross product with the vector.

Cross Product with the negative: For any vectors vec p, vec q
vec p xx (-vec q) = -(vec p xx vec q)

Solved Exercise Problem:

Given vec p xx vec q = -3i what is (-vec p) xx vec q?

• 3i
• 3i
• -3i
• i
• 3

The answer is '3i'

slide-show version coming soon