Projection Vector Proof

Projection Vector Proof

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

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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.

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7 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Cosine

Tangent

Sine

Secant

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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