Adding and subtracting vectors in component form

Adding and subtracting vectors in component form

In this section, we will learn how to find the sum, as well as the difference between vectors algebraically and graphically. We will do so with two methods – the "Tip To Tail" method, and the "parallelogram method.

Lessons

  • Introduction

  • 1.
    Given the vectors v=\vec{v}=<4,34,-3>, w=\vec{w}=<1,9-1,9> and t=\vec{t}=<2,52,5>,
    a)
    find v+v\vec{v}+\vec{v}

    b)
    find v+w\vec{v}+\vec{w}

    c)
    find 5v+2w+3t5\vec{v}+2\vec{w}+3\vec{t}


  • 2.
    Given the vectors v=\vec{v}=<5,55,5>, w=\vec{w}=<2,3-2,-3> and t=\vec{t}=<4,74,-7>,
    a)
    find vv\vec{v}-\vec{v}

    b)
    find vw\vec{v}-\vec{w}

    c)
    find 2vt3w2\vec{v}-\vec{t}-3\vec{w}


  • 3.

    Add and subtract vectors in component form
    a)
    find p+q\vec{p}+\vec{q} graphically and algebraically

    b)
    find 2q+p2\vec{q}+\vec{p} graphically and algebraically


  • 4.

    Adding and subtracting vectors in component form
    a)
    find pq\vec{p}-\vec{q} graphically and algebraically

    b)
    find q12p\vec{q}-\frac{1}{2} \vec{p} graphically and algebraically


  • 5.

    Addition and subtraction of vectors in component form
    a)
    find ab+c\vec{a}-\vec{b}+\vec{c} algebraically and graphically

    b)
    find 3ac+b3\vec{a}-\vec{c}+\vec{b} algebraically and graphically