What is the cross-product of the two vectors (1,2,3) and (4, 5, 6)? Make sure you do this one by hand. Input your answer in the form (*,*,*).

Question

BlackTom AI · Accepted Answer

To find the cross product of two vectors, we use the standard formula for a × b where a = (a1, a2, a3) and b = (b1, b2, b3): a × b = (a2*b3 − a3*b2, a3*b1 − a1*b3, a1*b2 − a2*b1).

Here, a = (1, 2, 3) and b = (4, 5, 6).
- First component: a2*b3 − a3*b2 = 2*6 − 3*5 = 12 − 15 = −3.
- Second component: a3*b1 − a1*b3 = 3*4 − 1*6 = 12 − 6 = 6.
- Third component: a1*b2 − a2*b1 = 1*5 − 2*4 = 5 − 8 = −3.

Therefore, the cross product a × b is (−3, 6, −3). This result can be obtained directly by expanding the determinant of the corresponding 3×3 matrix or by applying the component formulas above. The given coordinate form (-3,6,-3) matches this hand-computed result.

MTH1030 -1035 - S1 2025 MTH1030/5 MTH1030/5 Week 1 lesson quiz: Vectors, lines and planes

What is the cross-product of the two vectors (1,2,3) and (4, 5, 6)? Make sure you do this one by hand. Input your answer in the form (,,*).

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