Determine whether the vectors a = (1,2,3),b = (1,3,1),c =(2,2,2) plane? coplanar, that is, they lie in the same are

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

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

A:

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. 1= (-…

A: We have to solve given problem:

Q: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

A:

Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Find the vectors u and v whose initial point is u: (3, 2),v: (1, 4) and terminal points is (5, 6) ,…

A: Initial point is (3,2) and the ending point is (5,6) so the vector is u=(5,6)-(3,2)=(2,4)   Initial…

Q: Find a unit vector orthogonal to both u and v. (-3, 4, –2) (-1, 1, 0) u = V = 2 2 1 3' 3' 3

A: Given two vectors u and v, then the vector that is orthogonal to both u and v is their cross…

Q: Find the unit vector u in the direction of the vectorv=(-5, 12, 0).

A: Given          v =( -5, 12, 0 )

Q: Find the unit vector that has the same direction as vector v that begins at (1, 4, 10) and ends at…

A: We will find the unit vector that has the same direction with the given vector v in the following…

Q: Find two unit vectors orthogonal to both (2, 6, 1) and (-1, 1, 0)

A: The given vectors are The unit vectors can be obtained by the formula Now, find the cross product…

Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

A:

Q: Are vectors v = ⟨ − 2 , − 3 ⟩ and u = ⟨ 6 , − 4 ⟩ orthogonal? Yes or No:

A:

Q: ind a unit vector with positive first coordinate that is orthogonal to the plane through the points

A: Given that the plane passes through the points, P(4,1,-1) Q(5,2,0) R(5,2,5)

Q: Consider the vectors [2, 1,0,0], [3, 1,0,0], [0,0,0, 1] in R'. Find a vector v so that v, [2, 1,0,…

A: We know four vectors v1 , v2 , v3 and v4 in ℝ4  will be linearly independent iff , av1→ + bv2→ +…

Q: Calculate parallel component of vector a = [1,2.2] in the directoin of vector v = [7,7, 7].

A:

Q: The unit vectors normal to the vectors (2, - 8,11) and (- 3,0,5) are

A: Find unit vector

Q: Find two vectors of norm 1, orthogonal to all the vectors u = (2, 1, 4, 0), v = (−1, −1, −2, 2), w…

A: Given data:- u=2,1,4,0v=-1,-1,-2,2w=3,2,5,4

Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

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 area of the triangle with vertices (3, 7, 1), (4, 2, 1), and (3, 1, –6). Then find both…

A: Vertices of a triangle A(3, 7, 1), B(4, 2, 1), C(3, 1, -6) AB→=(4, 2, 1)-(3, 7, 1)      =1, -5, 0…

Q: Consider the vectors (2, 1,0, 0), [3, 1,0, 0], [0,0, 0, 1] in R". Find a vector v so that v,…

A:

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: 1. Express A = (3, 1, –1) as B+ C, where B is parallel to the vector (1, 4, 2) and C is…

A:

Q: Find two unit vectors orthogonal to both (1,-1,1) and (1,0,3)

A:

Q: Find two unit vectors orthogonal to a = (1, 1, 1) and b = (-4,0, 1) %3D Enter your answer so that…

A: Given,           a=<1,1,1> and b=<-4,0,1>

Q: Find two unit vectors orthogonal to a = (-2, 1, 0) and b = (-4,0, 1)

A:

Q: The cross product of vectors a = (-1, 4, 6) and b = (3, 0, -2) is %3D

A: The cross product of vectors is given below

Q: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…

A:

Q: Find two unit vectors orthogonal to both (3,2,1) and (–1,1,0).

A: The vectors 3,2,1 and -1,1,0

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…

A:

Q: Find two unit vectors orthogonal to a=⟨1,−1,−2⟩a=⟨1,−1,−2⟩ and b=⟨2,0,−2⟩b=⟨2,0,−2⟩.

A: Given vectors are

Q: Determine whether the vectors u = (-3,9,6) and v = parallel, (4, –12, –8) are orthogonal, or…

A:

Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: Show that the vectors , and are coplanar.

A:

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1).

A:

Q: What is the resultant of vectors a and b? (

A:

Q: Find the vector in R' from point A = (-2, –3, 8) to B = (9, –4,–3). AB = help (vectors)

A:

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u= (-11,0,5)…

A: To find the dot product and angle between the two vectors u and v.

Q: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

Q: Find the length of the vector. v = (5, 0, 3, -2) %3D ||v|| = %3D

A:

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: Determine the angle between the vectors a = (4, 5, 2) and b = (-3, 6, 0)

A:

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

A:

Q: Verify that the vectors a = (2, 5, –1) and b = (3, –1, 1) perpendicular. а. are

A:

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.