If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a + 3/4b and λa + b, find the value of λ if P, Q and R lie on a straight line.

Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

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Q: Given vectors v = (3, -1) and w = 1 (-4, 6), find 2v - 2W {8, -5) (4, -5) (-5, 4) (-8, 5) (-8, -5)

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Q: Suppose u = (-3, 2) and v = (10, 2) are two vectors that form the sides of a parallelogram. Then the…

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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: When analyzing the vector To the sum of two vectors, the first is parallel to the vector A = 2i-i+3k…

A: There is no specific formula.Please go through the solution.

Q: Given the vectors v=3i - 2j+5k and w=-i +4j+2k, find the following: a) 2v-w= b) V•W= ||w|| = c) 12 =…

A: v→=3i-2j+5k and w→=-i+4j+2k

Q: given the vector, PQ, whose initial point is P(-2,-5) and whose terminal point is Q(3,4) the…

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Q: If v=3w then the two vectors v and w are ................

A: Given :                    If v = 3w, then the two vectors  v and w are ____________

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: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find:

A: (a) The angle between the two vectors u and v is computed by the following formula. cosθ=u·v|u||v|…

Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

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Q: .If A = 2a, + a, - 3a, and B = 4ax + 2a, – 3a, are vectors, find (a) A· B (b) Á xB (c) Angle between…

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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: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

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Q: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

Q: Find the angle in degree between the two vectors as indicated in the rectangular box of dimension…

A: *to find:- angle between the vectors u & v.

Q: For each of the following vectors b€ Rª, decide whether b is a inear combination of V1, V2, and v3.…

A: We have to show whether the vector 'b' is a linear combination of v1,v2 and v3 where the vector are…

Q: 7. Find the values of m that will make the following vectors perpendicular. à = (2m, 3,1), b = (m,…

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Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: Given the vectors a=(-1,5,-4) and b=(2,-7,2) find the vectors x € R3 , with magnitude v371 and…

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Q: Given the points A: (1,6,3) and B: (2,-3,3), find the vector ü = AB %3D

A: To find- vector u.

Q: Suppose u = (0, –2) and v = (2, 2) are two vectors that form the sides of a parallelogram. Then the…

A: This question is based on parallelogram diagonal.

Q: Two vectors ñ and m are said to be parallel if n-m-0

A: False

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated list…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: 1. Assume the lengths of the vectors 2a – b and å + 35 , assuming å = (2,1,3) and b = (-1,2,2) 2. If…

A: Using scalar multiplication of vectors and magnitude of vector concepts  we can solve this question

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: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: To determine the value of b.

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

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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: Find the angle in degree between the two vectors as indicated in the rectangular box of dimension…

A: The dimension of the given box is 1×2×3.

Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

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 values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: It is known that any two vectors are orthogonal if their dot product is zero. The given vectors are…

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: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

Q: Find the vectors that satisfy the stated conditions. 23. (a) Oppositely directed to v (3,-4) and…

A: a) The given vector is v = <3, - 4>  To find vector opposite to given vector and half in…

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: 14. Given that a and bare two vectors, then the vector (a + b) × (a – b) is A. perpendicular to (a –…

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Q: ) Find the cross product of the given vectors e = (6,-2,3) and f= (2,5,-1).

A: Given that  e= (6,-2,3) and f= (2,5,-1). We find vector cross product of this given vector.…

Q: • (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and…

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Q: For the given vectors a and b, find the cross product a × b. a = (1, 0, -3), b =(3, 4, 0) axb=

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Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

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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.