O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

Q: Find the of A ABC Where the area vectors AC1,-1,1), B(2,1,1) and are cl-1,1, 2).

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: Given problem:- Determine the volume of the tetrahedron with vertices P(-4,4,0), Q(2,1,-3), R(1, 0,…

Q: ind a unit vector orthogonal to bothu and v. u = (-8, 7, -2) v = (-1, 1, 0)

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Q: ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA  respectively and are…

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Q: Let A=(−3,−5,0), B=(−2,−2,2), P=(k,k,k). The vector from A to B is perpendicular to the vector from…

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Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

Q: Find a unit vector perpendicular to both u = (2,3, –4) and v = (-1,1,–4). %3D

A: The unit vector perpendicular to u and v is given by: w=±(u×v)|u×v|

Q: Use vector method to find the area of the triangle with vertices A, B, C that shown in the figure…

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Q: 10. Find a unit vector in the same direction as PQ if P = (5, 4) and Q (3, 7). %3D

A: The solution is given as

Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: 24. Verify the parallelogram law for vectors u and v in R": |u + v|l° + |[u – v||² = 2||u||² +…

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Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

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Q: Qure O QY Use Gramer's Rule to Find Kyy and Z -y-22 = - %3D + 32 = 2 %3D 7X +y+Z = o %3D Q2/ Find…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges giver by the vectors u, v and w is…

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Q: Find all unit vectors perpendicular to (3,1,4) that make equal angles with j and k.

A: Here we have to find the all unit vectors perpendicular to (3,1,4) that make equal angles with j and…

Q: find the sum of vector AB and CD where A (1,-1) B (2,0) C(-,3) D(-2,2)

A: Let A (1,-1) B (2,0) C(-1,3) D(-2,2) be the given vector. Of course here in the problem   "-1"is…

Q: (a) Find the vector projection of a onto b , that is, find proj, a . (b) Find a vector in the…

A: We can solve the problem problem using concept of vector.

Q: Find Hhe voluie af Mee Parallelepiped daterimıned by he vectors a,b and c. (a) (,2,3)and…

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Q: , If P(2,-2,1) , Q(3, -1,2) and R( 3,-1,1) ノ a) find the area of the triangle determined by the…

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Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: We will use the given formula of volume to find the volume of the tetrahedron.

Q: A=4+J1 and B=2+j3 respectively determine the sum and the difference of the vectors in both…

A: Concept: Complex numbers: Complex numbers are two-dimensional complex or s-plane points that are…

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

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Q: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), af Find the unit vector orthogonat…

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Q: Describe the span ot the two vectors (1,0,9) and co. 1,15 geometricellyy in

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Q: Compute the cosine of the angle between the plane through P = (6,0,0), Q = (0,7,0), and R = (0,0,5)…

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Q: Find a unit vector (a) in the direction of u and (b) in the direction opposite that of u. Verify…

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Q: Let A=(0,−3,1), B=(−2,3,2), and P=(k,k,k). The vector from A to B is perpendicular to the vector…

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Q: After decompsing the Veclor A-2i-j+3k to Hhe Sum of tado vectors, the first is Parallel to the…

A: Every vector can be decomposed into two vectors. One vector is parallel to another given vector, and…

Q: ir kümelerinden kaç tanesi R' için bir tabandır? how many of the given vector

A: A subest S of R2 is a subspace if and only if it contains the null vector whenever it contains two…

Q: Qy: In VĘ CR) find all vectors which are orthegonal to u=(1,-2, 3) uut corath

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Q: tind a non-zero vector perpendıcular to the vectar u. Find the length of the vector R-

A: Consider two vector u→=ai→+bj→ and v→=ci→+dj→ if the two vector is perpendicular then the angle…

Q: Find the unit vectoru in the di rection of the vector v=4 (2, 1, 2). 1 u = u = В. 1 12 u = 1 u = 15…

A: v=4(2,1,2)v=(4*2,4*1,4*2)v=(8,4,8)Magnitude of vector|v|=(8)2+(4)2+(8)2=64+16+64=144=12unit vector u…

Q: How long is the vector v = (1, 1, ..., 1) in 9 dimensions? Find a unit vector u in the same…

A: Given: The vector v= (1, 1, 1, 1, 1, 1, 1, 1, 1).

Q: Compute the cosine of the angle between the plane through P – (6,0,0). Q = (0, 5,0), and R = (0,0,9)…

A: (a). Given points are P6,0,0, Q0,5,0 and R0,0,9. We know that equation of plane through a,0,0, 0,b,0…

Q: Suppose that u and v are two unit vectors in 3D and the angle between them 6 i. What is |u x v[? ii.…

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 3, 3), b = (-1,…

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Q: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

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Q: Let b = 4i + 3j and c be two %3D vectors perpendicular to each other in the xy-plane. All vectors in…

A: Given: b→=4i+3j and c→ are two vectors perpendicular to each other in xy-plane.  To find: All the…

Q: Find volume of the parallelepiped determined by the vectors a = (8, 1,0), E b = : (1,4, 1), and c =…

A: The given vectors are a=8,1,0, b=1,4,1 and c=1,1,10

Q: Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the…

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Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

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Q: a) tor which values on a are the vectors 87 2 -- a linearln independent?

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Q: Find the measure of the smallest nonnegative angle between the two vectors. Round approximate…

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Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: