Waste less time on Facebook — follow Brilliant.
×
Back to all chapters

Dot Product of Vectors

The dot product (also known as the scalar product) is an operation on vectors that can tell you the angle between the vectors.

Projecting a vector onto another vector

         

If the two vectors \( \vec{a} \) and \( \vec{b} \) are given by \( \vec{a} = 4i + 3j \) and \( \vec{b} = -3i + j, \) what is the difference between the length of the projection of \( \vec{b} \) onto \( \vec{a} \) and the length of the projection of \( \vec{a} \) onto \( \vec{b}? \)

A line \(l\) passes through the point \( P(0, 4).\) Let \( A\) and \(B\) be the two intersection points of \(l\) and the circle \( x^2 + y^2= 64 .\) If \(O\) is the origin and \( Q \) is the intersection point of the two tangent lines at points \( A\) and \( B, \) what is the result of the dot product \( \overrightarrow{OP} \cdot \overrightarrow{OQ}?\)

Project \(\vec{ u} \) onto \( \vec{v}, \) both defined below, and write the resulting vector in the same form as \( \vec{v}:\) \[ \vec{u} = i - 2j \text{ and } \vec{v} = -10 i. \]

Calculate the vector projection of \( \vec{a} = (-2, 3) \) onto \( \vec{b} = (6, 8). \)

If the two vectors \( \vec{a} \) and \( \vec{b} \) are given by \( \vec{a} = 3i + 4j \) and \( \vec{b} = -2i + 4j, \) what is the difference between the length of the projection of \( \vec{b} \) onto \( \vec{a} \) and the length of the projection of \( \vec{a} \) onto \( \vec{b}? \)

×

Problem Loading...

Note Loading...

Set Loading...