Projection Vector Proof

The video tutorial explains how to derive the formula for the projection vector of one vector onto another. It begins by introducing two generic vectors, a and b, and poses the question of how much of vector a is in the direction of vector b. The tutorial constructs a right-angle triangle to find the projection vector, named u, and explains the process of determining its magnitude and direction. The magnitude is derived using the cosine of the angle between the vectors, while the direction is determined by the unit vector of b. The final formula for the projection vector is presented, and the video concludes by discussing the symmetry in projection vectors.

What is the initial step in finding the projection of vector a onto vector b?

• Finding the midpoint between a and b

• Calculating the cross product of a and b

• Constructing a right angle triangle

• Drawing a perpendicular line from a to b

Which trigonometric function is used to relate the magnitude of the projection vector to the vectors a and b?

• Cosine

• Tangent

• Sine

• Secant

How is the direction of the projection vector determined?

• By using the cross product of a and b

• By finding the unit vector of b

• By calculating the angle between a and b

• By using the magnitude of a

What is the formula for the projection of vector a onto vector b?

• a cross b divided by the magnitude of a squared

• a dot b divided by the magnitude of b squared times vector b

• a cross b divided by the magnitude of b squared

• a dot b divided by the magnitude of a times vector a

What is the formal mathematical notation for the projection of a onto b?

• dot(a, b)

• u(a, b)

• proj(a, b)

• vec(a, b)

How can the projection of b onto a be derived?

• By finding the midpoint between a and b

• By using the same process as for a onto b

• By using the inverse of the projection formula

• By calculating the cross product of a and b

What is the significance of the symmetry in the projection of vectors?

• It simplifies the calculation of cross products

• It allows for the use of the same formula for both projections

• It negates the need for unit vectors

• It ensures the vectors are perpendicular