43. Three particles of mass 5 kg, 3 kg and 7 kg are placed at points A, B and C respectively whose position vectors are (i – 2j), m (7i + j) m and (-3i +Sj) m respectively. The position vector of their centre of mass is A (- +) m B (-1-#1) m 28 15 28 c (i+) m 28 (Gi-#) m D

Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

A:

Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

A:

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

Q: Pls help ASAP

A: It is vector problem

Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: 5- The value of the chiral vector of SWNTS if the n=8, m=6 and the first vector length equal to +1…

A: n=8 m=6

Q: (a) What is the sum V of the twelve vectors that go from the center of a clock to the hours 1: 00,…

A:

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

A:

Q: 4. Given the two vectors rA =-ax - 3ay - 4az and re= 2ax + 2ay + 2 az and point C (1, 2, 3) find: a)…

A:

Q: 2. Express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of…

A: position vectors

Q: 2. If a --i+3j-k and E-2itj-3K decompose vectoes E into the sum of two vectors, one is paralled and…

A: This question can be solved using the concept of condition of two vectors to be parallel and…

Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

A:

Q: 19. Find two unit vectors perpendicular to vector u= (7, 0, -1) and vector v = (1, -1, 1).

A: We have to find the unit vector

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

A:

Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

A:

Q: Let u = (1,2,-3,0) and v = (5,0,4,1) are vectors in R. Then the distance between u and v is:

A: Given The given values of u and v are and . Apply the Euclidean distance formula.

Q: 4. Four vectors are defined special unit vectors as ā- sĩ– 23+2k, b=27 –6K, www č--47 +3) and d -(x,…

A:

Q: 11) in triple cross of vectors (A × C) × B = Cx (B × A).

A:

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

A:

Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

A:

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: 9. Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R…

A: Since there is multiple questions, we will solve the first question. Repost the question again and…

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of vector

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: Please reply as soon as posible Consider the vectors u = (1, -8,5) and v = (- 15.0, -3) The vector…

A: Given vectors are u = (1, -8,5) and v = (- 15.0, -3)

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

A:

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

A:

Q: what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a…

A: A scalar is a real number. A scaler is a single, independent number.  A vector is a ordered…

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

A:

Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

A:

Q: What is the value of each of the constants that are part of the linear combination between the…

A:

Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: Find a nonzero vector u with initial point P(2,-3,6) such that: (a) u has the same direction as v =…

A: Find a nonzero vector u with initial point P(2,-3,6) such that: (a) u has the same direction as v =…

Q: 13. Describe the vector that translates LMN to L'M'N’. 6. L' L 2 N' M -6 -4 -2 4 6 N2 M -4 -6 4,

A: Translation vector

Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: 7. Find the cross product of the vectors (a) u=(1,2,-3) v=(-4,1,2) (b) u = (0,1,- 2) v = (3,0, - 4)

A:

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

A:

Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

A:

Q: 1. The path of a partide i3 qiven by Sut) =<3 lose, a thint 7 find a) Velouity vector and…

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

A:

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

A:

Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

A:

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: 10. The vectorj^3E is the same as vector O j^4E O j^5E O j^2E O jE

A: Solve by vector product

Q: 15.aib are in linearly independant vectors IK. et W= Span {aib, 2a+3b8. Tinen the dman sian )I B) 2…

A: Here, the vector 2a+3b is depending upon a and b. Therefore, any vector of W can be written as a…

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

A:

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.