Geometry

Dot Product of Vectors

Projecting a vector onto another vector

         

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

A line ll passes through the point P(0,4). P(0, 4). Let A A and BB be the two intersection points of ll and the circle x2+y2=64. x^2 + y^2= 64 . If OO is the origin and Q Q is the intersection point of the two tangent lines at points A A and B, B, what is the result of the dot product OPOQ? \overrightarrow{OP} \cdot \overrightarrow{OQ}?

Project u\vec{ u} onto v, \vec{v}, both defined below, and write the resulting vector in the same form as v: \vec{v}: u=i2j and v=10i. \vec{u} = i - 2j \text{ and } \vec{v} = -10 i.

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

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

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