Find the angle between the vectors r = (-1, 2) and s = (4, 2)

Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

A: Given: A→+B→=A→-B→ The magnitude of sum of A →and B→ is , A→+B→=A2+B2+2ABcosθ The magnitude of…

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: Find the dot product of the pair of vectors (-2, 5) and (4, 1).

A: Given : < -2 , 5 > and < 4 , 1 >

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

A:

Q: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

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Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: How is the angle between two vectors defined and how is it computed?

A: the angle between two vectors is computed using cosθ

Q: Find the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

Q: Find two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ while v2 is…

A:

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: Find two vectors v1 and v2 whose sum is (2, –5), where vj is parallel to (5, 2) while v2 is…

A:

Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

A:

Q: Find two vectorsī and 02 whose sum is (2, –4), where v, is parallel to (2, -4) while vz is…

A: We have to find vector v1 →and v2→   the sum of vector v1 →and v2→ is 2, -4   vector v1 →is parallel…

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

A:

Q: Find the vector with length V17 and same direction as = (7,0, -6).

A:

Q: How do you find the cross product a x b of two vectors if you know their lengths and the angle…

A: If you know the length of the two vectors a and b then, you essentially know |a| and |b| And then…

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Find two unit vectors orthogonal to both u→=⟨3,4,1⟩ and v→=⟨0,3,3⟩.

A:

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

A:

Q: Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to the…

A: follow next step

Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

A:

Q: Find the smallest positive angle between the given pair of vectors. (3,1) , (4,6)

A: The given pair of vectors are,

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: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: *

A: Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3

Q: Find the angle between the vectors u and v if u = (2,3,5) and v = = (1,–4,3) in

A: First we convert this into vector then find the angle

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: The scalar product of two vectors is defined as the product of their magnitudes times the of the…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

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

A:

Q: Find two vectors and 02 whose sum is (2, –4), where is parallel to (2, -4) while vz is perpendicular…

A:

Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

A:

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (2, −1, 0), v = (−1,…

A:

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

A: Unit Vectors orthogonal to vectors  <2,3,1> and <-1,1,0>…

Q: Find the angle between vectors v = (1,2,3) and w = (2 -1, 4)

A:

Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the vector of velocity which has a speed of (90m/sec) and parallel to the vector joining the…

A: Let Vector a is parallel to vector b then vector a = K Bn Where K is some constant and Bn is the…

Q: Find two vectors v1 and vz whose sum is (-4, –4, 5), where vj is parallel to (1, 1, –2) while v2 is…

A: we have to find the two vectors v1→ and v2→ whose sum is -4,-4,5 where v1→ is parallel to 1,1,-2…

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

A:

Q: Find two unit vectors orthogonal to a=⟨5,2,4⟩ and b=⟨5,0,4⟩ Answer so that the first vector has a…

A: We need to find a vector c→ , such thatc→ ⊥ a→ and c→ ⊥ b→ie,c→.a→ = 0  and c→.b→ = 0given,a→ = 5 i…

Q: Find two vectors ūj and īz whose sum is (-5, –3), where vj is parallel to (2, 5) while īz is…

A: To find - Find two vectors v1¯ and v2¯ whose sum is -5, -3, where v1¯ is parallel to 2, 5 while v2¯…

Q: Find two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: Find two vectors vj and 2 whose sum is (-2, -5), where is parallel to (-3, 4) while vz is…

A: Solution: The objective is to find the vectors

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

A:

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

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

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 two vectors and īz whose sum is (-4, -2), where vy is parallel to (-2, -5) while ū, is…

A:

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

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.