Calxsolver
Subject:  Linear Algebra

Cross product (1, 0, 0) × (0, 1, 0)

Two standard basis vectors give the third one via the right-hand rule.

Answer a × b = (0, 0, 1), a · b = 0, |a| = 1, |b| = 1, angle = 90°

Solution

  1. Vectors a = (1, 0, 0), b = (0, 1, 0)
  2. Magnitudes |a| = 1, |b| = 1
  3. Dot product a · b = 0
  4. Cross product a × b = (0, 0, 1)
  5. Angle between θ = arccos(a·b / (|a||b|)) = 90°

Try a similar problem yourself

Use the Vector Calculator to solve a similar problem with your own values.

Open the solver

More Linear Algebra problems

Determinant of [[3, 1], [4, 2]] Apply the 2×2 determinant formula det = ad − bc. Determinant of the 3×3 matrix [[1, 2, 3], [4, 5, 6], [7, 8, 10]] Use cofactor expansion along the first row. Multiply [[1, 2], [3, 4]] · [[5, 6], [7, 8]] Combine rows of A with columns of B to compute the product. Inverse of [[4, 7], [2, 6]] Check that the determinant is non-zero, then apply the 2×2 inverse formula. Inverse of [[2, 1, 1], [1, 3, 2], [1, 0, 0]] Use Gauss-Jordan elimination on the augmented [A | I] matrix. Add [[1, 2], [3, 4]] + [[5, 6], [7, 8]] Add two matrices of the same shape entry by entry.