Q2 A) Knowing that A = 2i + mj +k & B -5i +j+ 4k are perpendicular vectors. Find the value of m then find A x B

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

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: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i- 6j as…

A: Here we have to find the length of the diagonal.

Q: Find the value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

Q: The vectors A 5i + 7j – 8k and B 3i + yj + zk are known to be parallel. Find y and 2 y = = Z

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Q: If u = 5i - j+ k, v =j - 5k, w = -15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)…

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Q: Given the vectors, ū = -3i+2j and = 4i – j, find 4ü-27. %3D (-20,10) (20,-10) (-20,-10) (20,10)

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Q: Q3/B/ For what value of 2, the vectors 2i - j+ 2k and 3i + 22j are perpendicular?

A: We can use the concept of perpendicular vector their dot product is zero.

Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

A:

Q: Let u =j- 3k, v = - 9i + 3j – 3k, w = 3i -j+ k. Which vectors, if any are (a) perpendicular? (b)…

A:

Q: B- For what values of a1 are the vectors [a1,4,3] and [3,-2,12] are 1) Orthogonal? 2) Parallel? 3)…

A: Angle between two vector

Q: Given vectors u = 2xi + 9j and v = xi - 4j, find x so that u and v are orthogonal.

A:

Q: If a = 2i -j+2k and b =i+2j-2k, find two vectors c and d satisfying all the following conditions:…

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Q: given u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  determine a,b so that v are parallel vectors

A: Given that, u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  We have to determine a,b so that u and v are…

Q: For what value of (a) will the vectors V=-4i-8j+ak, U=2i+4j-5k are parallel?

A:

Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

Q: Let u= -10i+4j- 4k, v= 5i-2j+2k, w=2j-5k. Which vectors, if any are (a) perpendicular? (b) Parallel?

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Q: For what value or values of a will the vectors u = 2i + 4j - 5k and v = -4i - 8j + ak be parallel?

A: Given,

Q: Compute the dot product of the two given vectors: 27 1 3. Answer:

A:

Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: If a = 2i – j+2k and b =i+2j – 2k, find two vectors e and d satisfying all the following conditions:…

A: Let the required two vectors c and d be c=x1i+y1j+z1k and d=x2i+y2j+z2k. Now as per the given data,…

Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: Let u=j-5k, v=5i-j+k, w=-10i+2j-2k Which vectors, if any, are perpendicular? Which are parallel

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Q: 3 Consider the vectors a= =(2³₁) and b =(p+¹). 2p 8 Find the possible values of p for which a and b…

A: we have to find p.

Q: Find the dot product of the given vectors. ü =-i +5j v=-6i-2j u. v =

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

A: .

Q: Given the vectors u = -i-5j and v =-3i+2j, find u v

A: Given vectors are  u=-i-5j     and   v=-3i+2j

Q: Given v=[2,-9] and w = [7,-8], what is 2w-v written as a linear combination of unit vectors?  please…

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Q: Find the area of the triangle with two sides given by the vectors a = i – j+ 4k, and b = 2i – 4j+1k

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Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az * O…

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Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

Q: Q2/ A) Knowing that A 2i+mj+k & B-5i+j+ 4k are perpendicular vectors. Find the value of m then find…

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Q: Q3 - A//Find the value of M such that the vectors A 2i+ Mj+k and B = 4i-2j-2k %3D are perpendicular…

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Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A:

Q: Given the vectors v = 3i-8j and w = 6i-j, find 5v and v+w.

A:

Q: Q2/ A- If this vectors are perpendicular? Prove that. A-3i +j-4k B-2i- 2j + k B- Solve that

A: Two vectors are perpendicular if and only if their dot-product is equal to zero. Dot product of two…

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: Q2/ If A=ai+bj+3k, B= 2i+3j+4k, C-i+j+6k are vectors , perpendicular to B and A is perpendicular to…

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Q: Given the vectors v = 3i-8j and w =6i-j, find v W.

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

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Q: The value of A for which the vectors 2i- 4j + Ak and 3i- 6j + k parallel are

A: Given the two vectors Let's say v1 and v2 v1= 2i-4j+lemdak v2= 3i-6j+k

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: For the pair of vectors U = -2i + 8j, V = 2i + 8j, findU + V, U - V, and 4U + 5V. U + V = ( |)i+(…

A: We use the following formula to find the u+v: (ai+bj)+(ci+dj)=(a+c)i+(b+d)j

Q: 2. Square ABCD is drawn as showWn below with the diagonals intersecting at E. a. State four pairs of…

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Q: Find the value of a so that vectors U = ai + 12j and V = 31 + 9j are perpendicular. a =

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Q: In the following diagram, the rectangle ACEG is divided into four congruent rectangles. F E a) List…

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Q: b) For what values of A, the vectors 2i -j+ 2k and 3i + 22 j are perpendicular?

A: If we have two vectors ai^+bj^+ck^  and a'i^+b'j^+c'k^ , then, these vectors are said to be…

Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…

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.