The Vector Product. Remember that the scalar product is a number, not a vector Using the vector product to multiply two vectors, will leave the answer.

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Presentation transcript:

The Vector Product

Remember that the scalar product is a number, not a vector Using the vector product to multiply two vectors, will leave the answer in form of a vector. The good news is that you will not have to remember this formula

Rearrange the vectors as follows The vector product

One very important property of the vector product is: It will always be perpendicular to both vectors, a and b

Note that any combination of coordinates could have been used to find the normal vector, as well as any coordinates could have been used to find a value of k.

Angle between two planes

Point of intersection of a line and a plane The points of intersection can be found when the equation of the line is expressed in parametric form.

The angle between a line and a plane Note t hat we are using sin

Line intersection of two planes If two planes intersect, they intersect in a line. The parametric form of the line can be found as follows Using the parametric form, the equation of the line is

The shortest distance between the point and the line is therefore 7 units

The shortest distance between the point and the plane is therefore 15 units