Complete the sentence below. If v•w = 0, then the two vectors v and w are If v•w = 0, then the two vectors v and w are equivalent. congruent.

Q: If w = -2i + 6j, find the following vector: 2(-2) + 4(-6) W.

A: Given: The vector w=-2i^+6j^. w2 can be calculated as, w2=-22+622        =402       =2102…

Q: Which ONE of the following formulas involving vectors a, b.c, a # 0 is meaningless? A. B. Oc. (a…

A: We have to find which formulas involving vectors  a→,b→,c→ and vector a→ does not equal to zero…

Q: For the given vectors: å = (-2,-3), = (1,-2), č = (2,3), find: (a) 3ã – 5 + 2č (b) angle between the…

A: Vector: A quantity that has magnitude, as well as direction, is called a vector. The magnitude of a…

Q: If v = 7i + 3j and w = 4i - 5j, find each of the following vectors: a. v + w   b. v - w.

A: v=7i+3j  and  w=4i-5j   a. v+w=7i+3j+4i-5j=7+4i+3-5j=11i-2j

Q: Given the points A: (2,4,-3) and B: (2,-3,5), find the vector ā AB

A:

Q: Which of the following vectors are parallel? 1. Please select the two vectors that are parallel. А.…

A: 1) Two parallel vectors a and b are of the form a=kb, where k is a constant.  We can write <12,…

Q: Which of the following should be the number d for the vectors a = 2i-dj + 3k and b = 3i + 2j + 4k to…

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

A:

Q: Given vectors a= (2, 1) and b= (−3, 5), find −2a+4b. Write your answer in component form

A: To find the component form of a vector

Q: A If the magnitude of vector A is multiplied by 2, which of the following vectors would be the…

A:

Q: If P1 = (-2, 3), P2 = (-1, 5), and v is the vector from P1 to P2, a. Write v in terms of i and j. b.…

A: Given: P1=-2,3, P2=-1,5

Q: Given vectors: ū = (4, 9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R². b) Write u as…

A:

Q: If a and b are vectors then ||a × b||²+ (a .b)² OA. |la |||| OB. ||axb|| OC. Ja.b| OD. II

A: Given:-  a and b are vectors To find:- ||axb||2 +(a.b)2 = ?

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: If v = 5i + 4j and w = 6i - 9j, find each of the following vectors: a. v +w   b. v - w.

A: Given vectors:           v = 5i^ + 4j^and   w = 6i^ -9j^

Q: 19. Which of the vectors (A)–(C) in Figure 22 is equivalent to v – w? (A) (B) (C) FIGURE 22

A: The vectors substraction: (v-w)

Q: Given the vectors u = -i-4j and w=-2i+5j, find 7u and u – w. | Write your answers in the form ai+bj.…

A: Given the vector u = -i - 4j And w = -2i + 5j Find 7u and u - w in the form of ai + bj.

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

A:

Q: If U and W are unit vectors in R" and |U - 3W = v13, then the angle between U and W is: O a. 30° O…

A: Option C will be the right answer.

Q: Given the three vectors A = (3, 1, 1), B = (2, -1, 1), C = (0, 1, 2), find (AxB)xC %3D

A: The vector can be multiplied using the scalar product or dot product and vector product or cross…

Q: For vectors u, v, and w, which of the following expressions is incorrect (or does not make sense)?…

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

Q: For the given vectors: å = (0,3), b = (4, –2), ở = (3,2), find: (a) 3å – 6+ 2č (b) angle between the…

A:

Q: A B

A:

Q: 1) Which of the following expressions represent vectors? (Zero or more options can be correct) r a)…

A: Step:-1 Vector:- A vector is a quantity that has both magnitude and direction and vector is…

Q: If two nonzero vectors v and w are orthogonal, then the angle between them has which of the…

A: Two non-zero vectors v and w are orthogonal if angle between them is π2. The dot products of two…

Q: Given vectors 3 = (2, 1, 3) and w = (0, 1, – 1), answer the followings: (a) 7 . ở (b) ở × ở (c) ||27…

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Q: Given the vectors u= 6i-2j and v=-i+9j, find 3u and u+v. Write your answers in the form ai+bj. 3u =…

A:

Q: For what values of a and b are the vectors ; equal?

A: a-b2,  4a+b

Q: If v = 7i + 10j, find each of the following vectors: a. 8v    b. -5v.

A: The given vector is, v=7i+10j   Multiply the vector by the scalar quantity 8. 8v=87i+10j=56i+80j…

Q: Given vectors a = (-3,1,2), b = (4,0,-8), c = (6,-1,4) find a vector d that satisfies 4a - 2b + 2d =…

A:

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

A: Dot product of two vectors u and v is given by

Q: Given vectors a = (1,2, –1), b = (2,0,-1), and c = (2,2,1): a) What is 2ä – 35 + č? b) What is the…

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Q: Given the vectors u = and v= find each of the following: a) b) u•v c) ux v d) Proju v

A: The solution as follows :-

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: Suppose that A = 2i + j, B =i- 4j + k, and Ĉ = j+k. What is the magnitude of the vector 2Ã –B + Č?…

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Q: If A C =-8.4, A = 3i-4j, and C =6.5, the angle between the two vectors when they are drawn starting…

A: Let θ be the angle between the two vectors

Q: For the given vectors, a = 5i + 6j + 7k, b = 8i + j+ 3k and c = 2i + 3k, which statement is true:…

A: To DETERMINE :-  For the given vectors ,  a = 5i + 6j + 7kb = 8i + j + 3kc = 2i + 3k which statement…

Q: Find the vector −4v + 2w given the vectors v = 6i - 4j and w = −i + 2j. Write your answer in the…

A: The vector is given as :- −4v + 2w        The value of vectors v = 6i - 4j and w = −i +…

Q: For the vectors: (6, –5) and V = (-1,4) U = Which of the following is the correct value of: |3 7ỉ –…

A: Here we have to find |3u - 2v| using given u and v vectors

Q: For what values of a, b, and c are the vectors; Equal?

A: Given: 2a-ba-2b6, -22a+b-2c

Q: If u, v, and w are vectors in Rn n>=2, and c is a scalar, explain why the following expressions…

A: Concept:   A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Given the vectors v=7i-5j and w=−i+3j, find −9v and v-w. Write your answers in the form ai+bj.

A:

Q: For what values of a, b, and care the vectors (2a-b,a-2b,6) and (-2,2,a+b-2c) equal?

A: The given vectors are 2a-b,a-2b,6 and -2,2,a+b-2c . Note that, two vectors are equal if their…

Q: (2) The two vectors u and v are shown. (o) |v= 3 45° Ju|=2 (a) Find u v (b) Find v· u (c) Is u x v…

A: To find u. v,  v. u and( u x v).

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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Q: Let a and b be nonzero vectors in R³. Which of the following statements are true? (1) (a × b) · (3a…

A: Given data: The first given expression is (a×b)•(3a-b)=0. The second expression is a•b=0, then…

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.