We have two vectors: a= a-(:) and b=() What is the resultant of -a plus b?

Q: Find a unit vector that are orthogonal to the vector (2,−3,1), (5,−2,0), and (3,0,1)

A:

Q: Find the vector with length 3 making an angle of 7π/4 with the positive x-axis.

A: Given that the vector with length of 3 makes an angle of 7π/4 with the positive x-axis.

Q: If a vector gets multiplied by a positive number, its direction will be *.reversed FO TO

A:

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

A: I am assuming that our discussion is restricted to 2D geometry. A typical vector will have a…

Q: What is the zero vector?

A: We have to define

Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: Find two unit vectors parallel to (2, 3).

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Q: Find the vector of length 2 making an angle of 60° with the x-axis.

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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: Find a vector that has the same direction as 8i-j+4K but has a length of 6

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: The sum of the squares of the direction cosines of a vector in space add up to ..............

A:

Q: Find the vector in the direction of (5, – 12) with length 3.

A: To find: A vector in the direction of 5,-12 with length 3.

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

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Q: Find a vector of length 5 in the direction opposite that of (3, –2, V3).

A: Let the given vector be              a=3i-2j+3k The vector in the direction opposite to a  is  -a.…

Q: Which two vectors are perpendicular to both a and b?

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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: Find a vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

Q: Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

A: The given vectors are u=(0,1,1) & v=(1,0,1).

Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

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Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: What is the magnitude of the vector (2, 4, –4)?

A: FORMULA

Q: Find the vector that has the same direction as (6, 2, -3) but has length 2.

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Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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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: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: Find the angle between the vectors (-8, 1) and (5, 4). Carry your intermediate computations to at…

A: Let, the given vectors     u→=-8,1,  v→=5,4we have to find the angle between the vectors.

Q: Find the angle between the vectors (2, 1) and (3, -2) to the neareast second.

A:

Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: The orthogonal vectors are also independent.

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Q: he vector as a

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Express the vectors in terms of their lengths anddirections. -i - j

A: Given vector is: v = -i -j Then we get, The magnitude or the length is: = sqrt{(-1)^2+(-1)^2} =…

Q: Which two vectors are perpendicular to both å and b?

A: result of vector cross product of two vector is perpendicular to both the vectors.

Q: find two unit vectors orthogonal to (5,-5,3) and (-3,5,2)

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

A:

Q: A vector with magnitude 4 points in a direction 265 degrees counterclockwise from the positive x…

A: Given  Magnitude of 4 points at an angle of 265° In counter clockwise direction  from positive x-…

Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).

A: Explanation of the answer is as follows

Q: Find the angle between the vectors (-5, 4) and (-3, -1). Carry your intermediate computations to at…

A: Solution:

Q: when we decompose the vector , what would the vertical component be?

A: Use the decomposing concept of a vector.

Q: Find all vectors orthogonal to 3

A:

Q: Find the angle between the vectors [ -1, 1, 2] and [2,1,-1].

A: Consider the vector: v = −1,1,2w =…

Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

A:

Q: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

A: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.