Scalar Vector Multiplication Calculator

How it is calculated

Each component of the vector is multiplied by the scalar: k·(x, y, z) = (kx, ky, kz). The magnitude of the result is |k| × √(x² + y² + z²), so it is the original length scaled by the absolute value of k, never negative. The tool prints the new vector, that magnitude and the scalar, all rounded to two decimals.

All four fields (k, x, y and z) must be filled in; for a flat 2D vector, type 0 in z rather than leaving it empty, since an empty field gives no result. A scalar above 1 stretches the vector, between 0 and 1 shrinks it, a negative scalar reverses its direction, and 0 collapses it to the zero vector. Results are unitless: if the vector is in metres or newtons, the result is in the same unit.

Common mistakes

• Leaving z empty for a 2D vector. All components are required, so enter 0 for the missing one or the tool returns nothing.
• Expecting a negative magnitude when k is negative. Magnitude is a length and uses |k|; the sign of k shows up in the direction of the vector, not in its length.
• Treating this as a dot or cross product. Here k is a single number and the result is a vector of the same dimension, not a number or a perpendicular vector.
• Reading the Turkish-style output, such as (-6,00, -8,00), as a list of five numbers. The comma is the decimal mark, and components are separated by a comma and a space.
• Forgetting that components are rounded to two decimals in the display. A tiny result such as 0.004 × 2 appears as 0.01, though the exact value is kept inside the calculation.