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What is the geometric interpretation of the cross product of two non-zero vectors a and b?
What is the geometric interpretation of the cross product of two non-zero vectors a and b?
- They form two adjacent sides of a triangle.
- They form two adjacent sides of a quadrilateral.
- They form two opposite sides of a parallelogram.
- They form two adjacent sides of a parallelogram. (correct)
For two vectors a = and b = in V3, how is the cross product of a and b defined?
For two vectors a = and b = in V3, how is the cross product of a and b defined?
- As the product of the magnitudes of a and b.
- As the sum of the components of a and b.
- As the dot product of a and b.
- As a vector perpendicular to both a and b. (correct)
What is the determinant of a 2 × 2 matrix of real numbers?
What is the determinant of a 2 × 2 matrix of real numbers?
- The sum of the diagonal elements.
- The product of the off-diagonal elements.
- The product of the diagonal elements minus the product of the off-diagonal elements divided by 2.
- The product of the diagonal elements minus the product of the off-diagonal elements. (correct)
What is the determinant of a 3 × 3 matrix of real numbers defined as?
What is the determinant of a 3 × 3 matrix of real numbers defined as?
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When are two non-zero vectors a and b in V3 parallel?
When are two non-zero vectors a and b in V3 parallel?
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