How to Find Scalar Multiplication of Vectors?
Don't know how to scalar multiplication of vectors? The following step-by-step guide helps you learn how to find the scalar multiplication of vectors.
To multiply a vector by a scalar, multiply each component by a scalar. The product of a scalar with a vector is always a vector.
Step by step guide to scalar multiplication of vectors
The scalar component of the vector is multiplied by the scalar component of each component of the vector.
If \(u⃗=(u_1, u_2)\) has a magnitude of \(|u⃗ |\) and a direction of \(d\), then:
where \(n\) is a positive real integer, the magnitude is \(|nu⃗ |\) and the direction is \(d\).
If \(n\) is negative, the direction of \(n\)u is the total opposite of \(d\).
Properties of Scalar Multiplication:
Allow u and v to be vectors, and \(c\) and \(d\) to be scalars. Then the properties listed below are true:
Scalar Multiplication of Vectors – Example 1:
If u\(=(-2, 3)\), find \(6\)u.
Scalar Multiplication of Vectors – Example 2:
If a\(=3i+j+2k\), find \(5\)a.
Exercises for Scalar Multiplication of Vectors
- If a\(=(-1,-8)\), find \(4\)a.
- If v\(=6i-5j+4k\), find \(3\)v.
- If a\(=7, -3\), find \(-5\)a.
- If v\(=i-7j-5k\), find \(-6\)v.
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