How to Multiply Vectors

Vectors are important in physics.
••• Comstock/Comstock/Getty Images

A vector is defined as a quantity with both direction and magnitude. Two vectors can be multiplied to yield a scalar product through the dot product formula. The dot product is used to determine if two vectors are perpendicular to one another. On the other hand, two vectors can produce a third, resultant vector using the cross product formula. The cross product arranges the vector components in a matrix of rows and columns. It allows the student to determine the resultant force's magnitude and direction with little effort.

The Dot Product

    Compute the dot product for two given vectors a= and b= to obtain the scalar product, (a1_b1)+(a2_b2)+(a3*b3).

    Compute the dot product for the vectors a=<0,3,-7> and b=<2, 3, 1> and obtain the scalar product, which is 0(2)+3(3)+(-7)(1), or 2.

    Find the dot product of two vectors if you are given the magnitudes and angle between the two vectors. Determine the scalar product of a=8, b=4 and theta=45 degrees using the formula |a| |b| cos theta. Obtain the final value of |8| |4| cos (45), or 16.81.

The Cross Product

    Use the formula axb= to determine the cross product of vectors a and b.

    Find the cross products of vectors a=<2, 1, -1> and b=<-3,4,1>. Multiply vectors a and b using the cross product formula to obtain <(1_1)-(-1_4), (-1_-3)-(2_1), (2_4)-(1_-3)>.

    Simplify your response to <1+4, 3-2, 8+3>, or <5, 1, 11>.

    Write your answer in the i, j, k component form by converting <5. 1. 11> to 5i+j+11k.

    Things You'll Need

    • Pencil
    • Paper
    • Calculator

    Tips

    • If axb=0, then the two vectors are parallel to one another. If the multiplied vectors do not equal zero, then they are perpendicular vectors.

Related Articles

How to Find the Area of a Parallelogram With Vertices
How to Find Mass in Weight
To Calculate Arcsine, What Buttons Do You Press on...
How to Calculate Moles from Molecular Weight
How to Convert Seconds Into Miles Per Hour
How to Find the Distance of Y in a Right Triangle
How to Find Y Value for the Slope of a Line
How to Find the Area of a Parallelogram
How to Factorise a Quadratic Expression
How to Find a Vector That Is Perpendicular
How to Convert FT LB to IN LB
How to Convert a Load to PSI in a Tensile Test
How to Find the Cotangent on a Graphing Calculator
How to Convert Pounds Per Square Foot to PSI
How to Calculate the Area of a Pipe
How to Calculate the Degree of Polymerization
How to Write an Equivalent Fraction With a Given Denominator
How to Calculate the Volume and Circumference of a...
How to Calculate Peak Torque