Two vectors 2a − 3b and 3a − b are perpendicular. Find the angle, ?, (correct to the nearest degree) between a and b such that 0deg ≤ ? < 180deg and |a| = |b|.

Q: Show that each pair of vectors is perpendicular.     -4i -3j and 6 i - 8j

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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: The vectors (3, 6) and ( — 2, k) are parallel. Find the value of k

A: Given:3, 6 and -2,k

Q: Use vectors to find the lengths of the diagonals of the parallelograr that has i +j and i – 18j as…

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Q: a = 8i-j+ 4k, , b=4j + 2k Find the angle between the vectors.( First find an exact expression and…

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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: A. Find the values of x such that the angle between the vectors and is 45. B. List four main…

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Q: The sides of a rectangle are formed by vectors A and B with |A| =2 and |B| = 5. Determine the area…

A: topic - vectors

Q: a) Let a = 2i – 3j + xk and b = -3i + j + xk. Find the values of x for which vectors a and b are at…

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Q: a – ° and For what values of a and b are the vectors 2 4 equal? a +b

A: Given vectors are: a-b2 and 4a+b. To find values of a and b for which vectors are equal. Solution:…

Q: The vectors (8, 6) and (12, k) are parallel. Find the value of k.

A: Consider the given vectors, 8, 6 and 12, k here the objective is to find the value of k if the…

Q: . Given a and b are unit vectors, and the angle between them is 60deg , determine the value of |2a −…

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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: Two non zero vectors a and b have respective magnitudes a and b , respectively. Given that c = a×b…

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

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Q: 02. Given the vectors : A = (3.-1, 2), B = (0, 1, 1) and C- (2, 2,-1), find: the angles between the…

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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…

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Q: Let ABCD be a parallelogram 1. Express AC in terms of AB and BC 2. Express AC in terms of AB and CD…

A: Consider the given figure.

Q: GIVEN vectors 9. and 4 95, ind . Provide your answer belowe

A: Vectors u=&lt;9,2&gt;  and v=&lt;4,-9&gt; Given two vectors and find the cross product of both…

Q: Determine whether the planes are parallel, perpendicular, or neither. 7x + 28y - 21z = 1, -3x + 6y +…

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Q: 5) 5 li) Given that the vectors a and b are parallel, find the value of x when ()- 4 a and b = 8…

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Q: Find the angle between  the two vectors  v1 = and  v2 = give the answer in degrees, rounded to…

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Q: For what values of a and b are the vectors (a-b,2) and (4, a+b) equal? For what values of a, b, and…

A: Two vectors are equal if the corresponding components are equal . The vectors a-b,2=4,a+bif a-b=4…

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: Show that the pair of vectors is perpendicular. -2i - 5j and 10i – 4j To show that -2i – 5j and 10i…

A: Given,            To show that -2i -5j and 10i - 4j are perpendicular.

Q: With the given the three vectors A, B, C. Determine the dot product of vector A and C A= 2i - 3j +…

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Q: Verify that the vectors a, b, and a + b satisfy the triangle inequality. Since ||a + b|| - , and…

A: Given: a= 2i+jb=i+3j

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Q: 348, 7.) x and y are vectors between them and 2, respectively, with an angle of 120° of 3x + 27. the…

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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: Show that the pair of vectors is perpendicular. −2i − 3j and 6i − 4j

A: To show that −2i − 3j and 6i − 4j are perpendicular, we must show that their dot product equal to…

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

A: False

Q: Show

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Q: 36) Find the values of x and So the vectors 2i+3 and xi +4j are equal.

A: Two vector are equal if and only if their magnitude are equal and have same direction.

Q: Q2: There are two vectors (V, and V2). V, has length equals to twice the length of V2. If the angle…

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Q: Two vectors are defined as A = ax + 2ay + 3az and B = 3ax + 2ay -7az . Which of the following vector…

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Q: The vectors a and b are defined by a =1. b = . where reR. (a) Find and simplify an expression for a…

A: Solution:

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

A: Given vectors, a= 5c+3d b= 2c-d

Q: Determine the magnitude of the vector a+b and the measure of the angle between the vectors a and…

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Q: Given vectors đ = (2, – 2,–2) and b = (4,0,– 1), find 3đả +2b Select one: (6, -2, -3) (16, -4, -7)…

A: According to question given that a→=(2,-2,-2)b→=4,0,-1We have to calculate 3a→+2b→

Q: Three vectors A, B, and C are related as follows: AB = 24180°, A + C= -5 + 15i, and C is the…

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Q: If the vectors a and b are such that |a| |b| = -5, and a b = 10, then the angle between the two…

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Q: : There are two vectors (V, and V2). Vi has length equals to twice the length of V2. If the angle…

A: given there are two vectors, V1 &amp; V2. V1 has length equals to twice the length of V2. Angle…

Q: If two vectors a+b and a-b are parallel, then a and b are parallel. Select one: O True O False

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Q: Two non zero vectors a and b have respective magnitudes a and b , respectively. Given that c = a × b…

A: To show that,

Q: Given 2D vectors a and b such that |a|= 7 and |b| = 8 find the angle between the vectors if: a) |a…

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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: Show that each pair of vectors is perpendicular.     -6i -5j and 10 i -  12 j

A: If two vectors A and B are perpendicular then its dot product A.B=0Dot product:i, j,k are the…

Q: Let a, b, and x denote vectors in R,,. (a) Simplify 3a + (5b -2a) + 2(b - a). (b) If 5x - a = 2(a +…

A: (a) Calculation: The simplified form of 3a+5b-2a+2b-a can be obtained as,…

Q: Solve the problem. Which of the following vectors is parallel to v = 9i + 5j? 15 W = - 25 3. W = 15…

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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.