How do I teach students to map coordinates on to vectors?

Q: What is a vector?

A: A quantity that has magnitude as well as direction is called a vector.

Q: What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the…

A: Consider the provided information, The component vector v=PQ→ where P=a1,b1 and Q=a2,b2 are…

Q: What is meant by the term translation in vectors?

A:

Q: On the diagram to the right, what are the components of the resultant of the three vectors shown? *…

A: We have three vectors, two of them are in horizontal direction, 6 N is -x direction and  14 N in +x…

Q: What is the difference between a vector and a scalar?

A:

Q: How do you determine if two vectors are orthogonal?

A: If we are given two different vectors , then they are orthogonal if they are  perpendicular to each…

Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

A:

Q: How do you find the vector from one point to another?

A: The vector from one point to other is the difference between similar coordinates of two points.

Q: What is the vector between the point (−3a,−7b) and the point (−4a,−5b)?

A: Vector between two points A and B is B-A

Q: What are the unit vectors in their component form?

A: Write the definition of the unit vectors that help to find their component forms. A vector is said…

Q: Explain when a projection vector is negative, positive, or zero.

A: This question is based on dot product of two vector.

Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

A:

Q: Explain how to write a vector in terms of its magnitude and direction.

A: A vector is a geometric representation of magnitude and direction with respect to the set of…

Q: We say that two vectors are equivalent .if they have the same components

A: Ginen statement, Two vectors are equivalent if  they have same component.

Q: How can we find the cartesian equation from a vector equation?

A: Equation of line in vector form is:r→=a→+λb→Where,a→=x1i→+y1j→+z1k→ b→=b1i→+b2j→+b3k→

Q: Resolve the vector of 300N at N25W into its rectangular components. Use right/left and up/down for…

A: Vx = -126.785 Vy = 271.892   explanation is given in below step

Q: Determine the tail of the vector whose head is(1, 2). Make a sketch.

A: Given the vector 26 and tail of the vector is (1,2). We need to find the head of the vector.

Q: What is the vector shown in component form? Enter your answer by filing in the boxes.

A: Consider the vector

Q: Find the dot product of vectors and .

A:

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: how can i learnd about vector in r2 and r3?

A:

Q: Explain how you can convert from a plane's scalar equation to a vector equation.

A:

Q: Explain with the help of an example whether the angle between vectors is acute or obtuse.

A: As the Angle Increases, the Name Changes: Type of Angle Description Acute Angle is less than…

Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: Find a vector in the same direction as (-5, 2, –3) with magnitude 6.

A: In this question , firstly we can find the unit vector of the given vector and after that we can…

Q: The ________ ________ of two vectors yields a scalar, rather than a vector.

A: Given as  The ________ ________ of two vectors yields a scalar, rather than a vector.

Q: Determine the head of the vector;whose tail is (−3, 2). Make a sketch.

A: Consider (x, y) as the head of the vector. Then  -25=xy--32-25=x+3y-2

Q: he vector as a

A:

Q: How can you tell when vectors span a certain R^? Please explain in the most simplistic detail>

A: Let S=v1,v2,v3 And v1=1-12;v2=213;v3=-102 Does SpanS=ℝ3? if any vector in ℝ3 can be expressed or…

Q: How would I write this vector in component form?

A: Given, Magnitude A=6 unit Direction A is θ=265°

Q: Determine the tail of the vector whose head is (1, 2). Make a sketch.

A: Consider the provided vector, 26 Whose head is 1,2. Determine the tail of the given vector.

Q: How do I solve these questions using vectors?

A: As per our company guidelines we are supposed to answer only first sub-parts. Kindly repost other…

Q: set

A:

Q: What is the equation of the vector in a Cartesian coordinate system that originates from the origin…

A:

Q: Determine the angle that the vector [- /3, – 1] makes with the positive horizontal X - axis

A: To find the angle between the vector -3,-1 and positive x-axis

Q: 1. What is the appropriate dot product technique for both Cartesian and Geometric vectors?

A: Given

Q: How could you describe vector subtraction geometrically?

A: We have write about  vector subtraction geometrically

Q: How do we know if two nonzero vectors are perpendicular?

A: Two non-zero vectors are perpendicular if their dot product is zero.

Q: Find the component form and magnitude of vector v. 7. Initial Point (12,-3) Terminal Point (4,-1)

A: We can find the answer as below

Q: What is the component form of the vector represented by 2a when = (-2, 3)? Enter the answer in the…

A: If we multiply by a constant to any vector then  magnitude of that vector will be changed.

Q: Find a unit vector perpendicular to both (3,-2,4) and (-1,2,-3).

A:

Q: I used a vector to represent a wind velocity of 13 miles per hour from the west.Determine whether…

A: Reason: (i)  When a velocity of a wind travels from the west and from the east of…

Q: find the component form of the vector. The vector from the point A = (2, 3) to the origin.

A: Find the component form of the vector. The vector from the point A = (2, 3) to the origin.

Q: What is a position vector?

A: What is a position vector?

Q: What are parallel vectors?

A: We have to define parallel vectors. Two vectors are said to be parallel if they have same direction…

Q: Explain how to add vectors.

A: vector:  a quantity which has magnitude along with direction is a vector. vector addition:…

Q: Explain Properties of Vector Operations?

A: Query- Explain Properties of Vector Operations. Answer- There are two things required to defne a…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.