The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1 : 4, 3 : 2 and 3 : 7 respectively. Show that there exists a point G such that the sum  of the vectors AD, BE, CF is parallel to CG. What ratio does G divide AB?

Q: Given the vectors r,=3i-2j, r2=i+3j, r3=3i-2j, r4=-i+2j, Indicate if these vectors are parallel,…

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Q: .If the position vectors of the points A, B, C, D are a = i+j+k, b 2i + 3j, c= 3i+ 5j - 2k, d k-j.…

A: Given:  a=i+j+k, b=2i+3j, c=3i+5j-2k, d=k-j We know that if A=x1i+x2j+x3k, B=y1i+y2j+y3k then…

Q: 10. In the figure here, D is the midpoint of side AB of triangle ABC, and E is one-third of the way…

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Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: For what value of m, the vector 4i + 2j – 3k and mi - j+ 3k have same magnitude? Given the points A…

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Q: Given that vectors p and q are perpendicular, where p≠0 and q≠0 show that |2p+3q|²= 4|p|²+9|q|²

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Q: If the position vectors of the points A, B, C, D are a = i + j + k, b = 2i + 3j, c = 3i + 5j − 2k, d…

A: Consider the vectors: a=i+j+k……1b=2i+3j……2c=3i+5j-2k……3d=k-j……4

Q: Given vectors: A(6.4,3), B(0.4.6) and C(8.2.1) forms a triangle. Find the angle at point B

A: Solution

Q: For the vectors v= (3,2)  and w= (-4,1) : What is the angle between v and w? Show all work.

A: According to our company's guidelines, I can only answer first question since you have asked…

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Q: If la| = v2, la + b| = v6 and la – b| = v2, find the angle between the two vectors å and b.

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Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1:4, 3:2 and 3:7…

A: If the position vectors of A and Bare a→ and b→ then the position vector of point P divid.ing AB in…

Q: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

Q: Given vectors ū = [3,2, –1] and v = [-2,2,4] , calculate the following: %3D %3D a) 2ū + 30 b) ū · v…

A: Use vector properties.

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

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Q: Let the angle between two nonzero vectors u and V be 45°, the magnitude of the vectors be a and 2…

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Q: If u, v and w are mutually perpendicular vectors, which of the following would not be true? O a) v•…

A: Given  vector u v and w are mutually perpendicular  .  ie .    u.v=v.w=u.w=0

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

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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,

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Q: In the diagram, ABC is an equilateral triangle, and D, E and F are the midpoints of its sides. As a…

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Q: Given the vectors: u = (-6,0,9), v = (7,-5,–1) and w = (1, 1,8), (a) Find the measure of the angle…

A: Given vectors: u→=<-6,0,9>v→=<7,-5,-1>w→=<1,1,8> To measure the angle between v…

Q: Given the vectors: Given the vectors u = 3i + yj ; v = 5i + 5j ; Determine which of the following…

A: topic - vectors

Q: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

Q: If the position vectors of the points A, B, C, D are a = i +j+k, b = 2i+ 3j, c = 3i+ 5j – 2k, d= k –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

Q: Given that the vectors a=(6,-1,2k)  and b=(-1,k+1,4) are perpendicular, what is the value of k?

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Q: Find the magnitude of each of the two vectors a and b having the same magnitude such that the angle…

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Q: Given the lengths of two vectors, namely, |u| = 1 and |v| =2, find the the dot product of u + v and…

A: answer is in next step.

Q: Given points: A = (4, 9, 1) B = (-2, 6, 3) C = (6, 3, -2) Using angles between located vectors,…

A: the given vertices are if the dot product of any two vectors is zero then we can say that A, B, and…

Q: Given that u and v are two vectors in R" with ||u|| = 10 and ||v|| = 7. (a) Find the maximum and…

A: The given problem is to find the maximum and minimum values of the given vector and also find the…

Q: 9. The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1:4, 3:2 and 3:7…

A: Given: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1:4, 3:2 and…

Q: The points D, E, and F divide the sides BC, CA, and AB of a triangle in the ratios 1:4, 3:2, and 3:7…

A: The points D, E, and F divide the sidesBC, CA, and AB of a triangle in the ratios 1:4, 3:2, and 3:7…

Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

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: In the rectangular prism shown below, OA=a, OC=b and oD =c. Express each of the following vectors in…

A: We have to express sides of rectangular I  prism in terms of vector a, b, and c

Q: The angle between the vectors a=(2,6) and b=(3,-1) is :إختر أحد الخيارات а. 4 b. С. 3 d. 2

A: The required angle is, option (b) π/2 The detailed solution is as follows below:

Q: Given the vectors v = 2i+ 3j – k and w = 4i – 2j + 3k. Find the angle between v and w. %3D

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Q: An angle in standard position lies in 2nd quadrant, and the point Q on its terminal side has radius…

A: The distance along the y-axis is called the ordinate.

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A: Given, 2a→∧b→∧b→∧c→ Let, 2a→∧b→=u→ Now simplifying the given equation by apply the vector dot…

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A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: For what values of ai are the vectors [a1,4,3] and [3,-2,12] are a) orthogonal? b) Parallel? c) Have…

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Q: ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD. Vectors

A: Consider the given information. Let's draw the triangle.

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Q: and b are two unit vectors such that + 2b and 5 a. 4 b are perpendicular to each other, then the…

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Q: Given the triangle with vertices A=(1,2,3), B=(3,-1,0), and C=(4,1,2), find unit vector of BM, i.e.…

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Q: 8. In triangle ABC, the point D is the midpoint of BC and E the midpoint of AC Vectors are marked as…

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Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1 : 4, 3 : 2 and 3 :…

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Q: If the vectors in the figure satisfy Ju| = |v| = 1 and u + v + w = 0, what is |w|? u |w| =

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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.