Vectores en R2^2

Multiple Choice

What is the topic of UNIDAD 2?

• Vectors in R^2

• Matrices

• Calculus

• Statistics

Multiple Choice

What are the main components of vectors in the plane?

• Magnitude and direction

• Types and operations

• Dot product

• All of the above

Multiple Choice

What is the definition of a vector in the plane R2?

• A vector is a point in R2

• A vector is a line segment

• A vector is a direction

• A vector is a point in 3D

Multiple Choice

Demonstrate that the vectors u = (2, -3) and v = (-4, 6) are parallel.

• By calculating the dot product

• By finding the magnitudes

• By checking the angles

• By using the cross product

Multiple Choice

What is the formula for the vector PQ given two points P(x1, y1) and Q(x2, y2)?

• PQ = (x2 - x1, y2 - y1)

• PQ = (x1 + x2, y1 + y2)

• PQ = (x2 + x1, y2 - y1)

• PQ = (x1 - x2, y1 + y2)

Multiple Choice

Given points P and Q, calculate the vectors PQ and QP.

• PQ = (2, 1)

• QP = (-2, -1)

• PQ = (2, 2)

• QP = (0, 1)

Multiple Choice

What does the direction of a vector represent?

• The angle formed with the positive x-axis

• The length of the vector

• The position of the vector

• The color of the vector

Multiple Choice

What is the definition of a vector in the plane xy?

• A pair of ordered real numbers (a, b)

• A single real number

• A geometric shape

• A point in space

Multiple Choice

Calculate the magnitudes of the vectors i) v = (2, 2); ii) v = (2, 2√3); iii) v = (-2√3, 2);

• v = √2 + 2 = √8 = 2√2

• v = √2 + (2√3)² = 4

• v = √(-2√3)² + 2² = 4

• v = √(2)² + (2)² = 4

Multiple Choice

What is the formula for calculating the magnitude of a vector between two points P1 and P2?

• √((x2 - x1)² + (y2 - y1)²)

• (x2 - x1) + (y2 - y1)

• (x2 + x1)² + (y2 + y1)²

• √((x1 - x2)² + (y1 - y2)²)

Multiple Choice

What is the formula for the dot product of two vectors A and B?

• A · B = x1 + y1

• A · B = x1 * x2 + y1 * y2

• A · B = x1 - x2 + y1 - y2

• A · B = x1 / x2 + y1 / y2

Multiple Choice

What is the formula for calculating the cosine of the angle between two vectors u and v?

• cos φ = u · v / |u||v|

• cos φ = |u| + |v|

• cos φ = u + v

• cos φ = |u| - |v|

Multiple Choice

¿Cómo se define el ángulo entre dos vectores u y v?

• Como el ángulo más grande entre ellos

• Como el ángulo no negativo más pequeño entre sus representaciones

• Como el ángulo recto entre ellos

• Como el ángulo de 90 grados

Open Ended

Encuentre el ángulo entre los vectores u(2,3) y v(-7,1).

Multiple Choice

What are the conditions for two vectors to be considered equivalent?

• They must have different magnitudes

• They must have the same direction

• They must have the same magnitude, direction, and sense

• They must be perpendicular

Open Ended

Dado el vector \( \vec{u} = (2, -1) \), determinar dos vectores \( \vec{AB} \) y \( \vec{CD} \) equipolentes a \( \vec{u} \), sabiendo que A(1, -3) y D(2, 0).

Multiple Choice

Given the vector \( \mathbf{u} = (2, -1) \), determine two equivalent vectors \( \overrightarrow{AB} \) and \( \overrightarrow{CD} \) knowing that A(1, -3) and D(2, 0). What are the coordinates of point C?

• (0, 1)

• (1, 0)

• (0, 0)

• (1, 1)

Multiple Choice

Given the vector \( \mathbf{u} = (2, -1) \), determine two equivalent vectors \( \overrightarrow{AB} \) and \( \overrightarrow{CD} \) knowing that A(1, -3) and D(2, 0). What are the coordinates of point B?

• (3, -4)

• (4, -3)

• (2, -2)

• (1, -1)

Multiple Choice

What are the special vectors in R2 that allow representation of any other vector in the plane?

• i and j

• x and y

• a and b

• 1 and 0

Multiple Choice

What are the coordinates of points A, B, and C in the vector representation?

• A(4, 6)

• B(8, -2)

• C(-4, -1)

• D(0, 0)

Multiple Choice

What is a unit vector?

• A vector with length 0

• A vector with length 1

• A vector with length 2

• A vector with length 3

Open Ended

Demuestre que los vectores u = (2, -3) y v = (-4, 6) son paralelos.

Multiple Choice

What condition must be met for vectors u and v to be orthogonal?

• u · v = 0

• u · v = 1

• u · v = -1

• u · v = 2

Open Ended

Demuestre que los vectores u = 3i + 4j y v = -4i + 3j son ortogonales.

Multiple Choice

What is the direction of the vector \( \alpha v \) when \( \alpha > 0 \)?

• Direction of \( v \)

• Direction of \( -v \)

• Direction of the origin

• Direction of the x-axis

Multiple Choice

What is the method used to sum vectors in the image?

• Parallelogram Method

• Triangle Method

• Graphical Method

• Algebraic Method

Multiple Choice

What is the resultant vector when combining vectors A, B, C, and D using the polygon method?

• Vector A

• Vector B

• Vector C

• Vector D

Multiple Choice

What does the commutative law of vector addition state?

• The order of addition does not matter

• Vectors can only be added in a straight line

• Vectors can be added in any direction

• The sum of vectors is always zero

Poll

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