Find the cross product of vectors (a × b) in 3D space

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Q1. If a=⟨1, 3, 4⟩ and b=⟨2, 7,−5⟩, find the cross product of a×b.

Not to be confused with the dot product, the cross product (also called the vector product) of two vectors in 3D space results in a vector rather than a number. The cross product of two vectors, a and b, produces a vector c that's perpendicular to both (this can easily be proven by taking the dot product).

The definition is provided below given a=⟨a_1,a_2,a_3 ⟩ and b=⟨b_1,b_2,b_3 ⟩.

( a×b=⟨a_2 b_3−a_3 b_2, 〖 a〗_3 b_1−a_1 b_3, 〖 a〗_1 b_2−a_2 b_1 ⟩ )

If you're familiar with finding determinants, another way to remember this formula is shown below:

Q2. Show that a×a=0 for any vector a in 3D.

When the cross product equals 0, it suggests the vectors are parallel.