If vector Vector a = (3, 2, 9), and Vector b = (-4, 7, 2), find Vector a × Vector b.
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To find the cross product of two vectors a and b, we use the following formula:
a × b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)
Given that Vector a = (3, 2, 9) and Vector b = (-4, 7, 2), we can substitute the values into the formula to find the cross product.
a × b = (3*7 - 2*2, 2*2 - 3*(-4), 3*(-4) - 2*7)
= (21 - 4, 4 + 12, -12 - 14)
= (17, 16, -26)
Therefore, Vector a × Vector b = (17, 16, -26).
To find the cross product of two vectors, you can use the formula:
Vector a × Vector b = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁)
Here, a₁, a₂, and a₃ represent the components of Vector a, and b₁, b₂, and b₃ represent the components of Vector b.
Given that Vector a = (3, 2, 9) and Vector b = (-4, 7, 2), we can substitute the values into the formula to find the cross product:
a₁b₂ - a₂b₁ = (3 * 7) - (2 * 2) = 21 - 4 = 17
a₂b₃ - a₃b₂ = (2 * 2) - (9 * -4) = 4 - (-36) = 4 + 36 = 40
a₃b₁ - a₁b₃ = (9 * -7) - (3 * -4) = -63 - (-12) = -63 + 12 = -51
Therefore, the cross product of Vector a and Vector b is (17, 40, -51).