What is the product? [3 6 1][-1 2 4] x [2 4 0] [0 6 2]
B. [1 26 7]
The given expression is a cross product of the two vectors:
[3 6 1] and
[-1 2 4]
and
[2 4 0]
[0 6 2]
The cross product of two vectors a and b is given by:
a x b = [a2b3 – a3b2, a3b1 – a1b3, a1b2 – a2b1]
Let’s calculate each component of the answer:
For the first component:
[3 6 1] x [-1 2 4] = (6 x 4) – (1 x 2) = 22
[0 6 2]
So, the first component of the answer is 22.
For the second component:
[-1 2 4] x [0 6 2] = (4 x 0) – (2 x 2) = -4
[2 4 0]
So, the second component of the answer is -4.
For the third component:
[2 4 0] x [3 6 1] = (4 x 1) – (0 x 6) = 4
[0 6 2]
So, the third component of the answer is 4.
Thus, the product of the two vectors is:
[22 -4 4]
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