Scalar multiplication

Scalar multiplication

We have learnt that for a vector arrow, the greater the length, the greater the magnitude. Now what if we somehow want to increase or decrease the magnitude of an existing vector? In this section, we will introduce scalar multiplication – a tool that allows us to lengthen or shorten a vector arrow, in other words, a technique that alters the magnitude of a vector.

Lessons

  • 1.
    Given that vector v=\vec{v}=<5,3> , determine 6v6\vec{v}

  • 2.

    Scalar multiplication
    a)
    determine 0p 0\vec{p}

    b)
    find the magnitude of 0p 0\vec{p}


  • 3.
    Given that vector w=\vec{w} = <10,410,-4>
    a)
    determine 12w\frac{1}{2}\vec{w}

    b)
    find the magnitude of 12w\frac{1}{2}\vec{w}


  • 4.

    Scalar multiplication
    a)
    determine 3t3\vec{t} and 3t||3t||

    b)
    determine 3t-3\vec{t} and 3t||-3t||


  • 5.

    Scalar multiplication
    a)

    Scalar multiplication

    b)

    Scalar multiplication