2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the angle between the two vectors? %3D

Q: A: Convert the point (4, 37) to Cartesian Coordinates B: Evaluate (u + 2w) x 3v were v =, i =, w w =

A: We will solve the problem

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: For what values of b are the given vectors o , (smallest value)

A: Let m→=-12, b,3 and n→=b, b2,b  If m→ and n→ are orthogonal.

Q: It is known that the area of the parallelogram P formed by the vectors u and V is 14 square units…

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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: Suppose that U and V are vectors of lengths 2 and 3, respectively. If the angle between U and V is…

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

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Q: 33. If 0 is the angle between two nonzero vectors v and w, and v· w < 0, what is the range of 0?…

A: Use the geometric definition of the dot product to calculate the angle between two non        zero…

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: 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: 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: If v × w =4i −j +k, and v⋅w=5, and θ is the angle between v and w, then tanθ = ? v and w are…

A: Given  v × w =4i −j +k, and v⋅w=5, and θ is the angle between v and w  Now we have to find tanθ as…

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

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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: What is the angle of vectors A=5m West and B=15m 60° North of West?

A: The vector A can be written as: a=-5i The vector B is 60 degree north of west that means it makes an…

Q: Suppose u = (-1.8,-2.1) and v = . Find the angle between the two (position) vectors u and v. Provide…

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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: The vectors A 6i + 4j – 8k and B = xi + 6j + zk are known to be parallel. Find x and z x = 9. -12

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Q: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

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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 length and direction (when defined) ofu * v and v * u. u = -8i - 2j - 4k, v = 2i + 2j + k

A: Given vectors - u = -8i-2j-4kv = 2i+2j+kPart (1) - u×v = -8i-2j-4k×2i+2j+ku×v =…

Q: If the points with position vectors 10i+3j.12i-5j and ai+11j are collinear, Find the value of a.

A: The position vectors of the points which are collinear is: 10i+3j ,     12i-5j ,      ai+11j

Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: The angle between the two vectors u = (4, 7) and v = (11 /2, 3 /2) computed via the cosine formula…

A:

Q: Find the angle in degrees between u = (1, 2, 0) and v = (1, -2, 1)

A: Given, u=1,2,0v=1,-2,1 The formula for finding the angle between the two vector is, cosθ=u→·v→u→v→

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i, v = -3j

A: Given vectors: u=2i+0j+0k and v=0i-3j+0k u×v=ijk2000-30u×v=i0×0-0×-3-j2×0-0×0+k2×-3-0×0u×v=-6k The…

Q: What is the angle of vectors A=5m South and B=15m 60° South of West?

A: `Vector is a quantity that has magnitude as well as direction. So we need to find the angle of…

Q: Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by…

A: A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A,…

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

A:

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: 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: Consider V=(6, -3) & W=(-4, 8) Find angle between the two vectors.

A: Recall: Angle between two vectors:     Let a→ and b→ be two vectors then,             cosθ=…

Q: For what values of b are the vectors (–88, 6, 7) and (b, b², b) orthogonal? Answer (separate with…

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Q: Let ā = (4, 3) and b = (– 4, 4). Find the angle between the vector, in degrees.

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Q: If u = 2i -j- 3k, w = 3i – 9j+ 5k and v = perpendicular. 15i – 3j – 5k, then the vectors are Select…

A: which option?

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

A: This question is taken from the vector in which we have to find the value of a for the different…

Q: Which vector is not collinear with [c, d]? O [2c, 2d] O(-c, -d] O [10c, 10d] O [d, c]

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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.

Q: Given that the angle between the nonzero vectors đ = (u,,u2,u3), b = (u3.U2, -u,) is find the…

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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: For what value of "c" are the following vectors perpendicular? 3 (2, с, 9) аnd ў 3 (Зс, —1,5) (Зс, —…

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Q: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

A: This question is related to vectors, we will use formula of dot product of vectors and basic…

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

A: We know, the angle between two vectors v→ and w→ is θ = cos-1v→·w→|v→| |w→|

Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

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

A: The given figure is:

Q: Which pairs of vectors are parallel? Select all that apply. OA. 10i – 15k, –4i + 6k В. 3і + 4j, —12i…

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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.