Calculator for multiplying a 4-dimensional vector and a scalar
This function multiplies a vector by a real number. To perform the calculation, enter the vector and the real number to be calculated and click the Calculate button. Empty fields are counted as 0.
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Vectors can be multiplied by real numbers. The real number is called a scalar to distinguish it from vectors.
If the scalar is positive, the resulting vector will point in the same direction as the original. If the scalar is negative, it points in the opposite direction.
Vector and scalar are multiplied by multiplying the individual elements of the vector with the scalar. Is calculated:
\(\displaystyle\left[\matrix{a\\b\\c\\w}\right] \cdot x = \left[\matrix{a \cdot x\\b \cdot x\\c \cdot x\\d \cdot x}\right]\)
\(\displaystyle\left[\matrix{2\\3\\4\\5}\right] \cdot 5 = \left[\matrix{2 \cdot 5\\3 \cdot 5\\4 \cdot 5\\5 \cdot 5}\right] = \left[\matrix{10\\15\\20\\25}\right]\)
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