Let u=j-5k, v=5i-j+k, w=-10i+2j-2k Which vectors, if any, are perpendicular? Which are parallel

Q: Determine whether or not the given two vectors are parallel.u =〈-3, 1, 4〉, v =〈6, -2, 8〉

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Q: The dot product of vectors p = (3, -5) and q = (15,9) is A/

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Q: or what values of aj are the vectors [ai,4,3] and a) orthogonal? b) Parallel? c) Have 45 degree…

A: If 2 vectors a⇀,b⇀  are orthogonal, their dot product a⇀.b⇀ =0 Let u=a1,4,3 and v= 3,-2,12 So,…

Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = 9i – 6j+ 3k, v =…

A: We will calculate the dot product and the angle  between these vectors to solve this question.

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: Suppose that u and v are vectors in R' both of length 2/2 and that the length of u – v is also2 /2.…

A: The solution is give as

Q: 5. Determine the value of a so that the vectors v = perpendicular. (a,3, -2) and v - (2, -2a, 1) are

A: Solve the following

Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: A. IF V = yi - x), find curt(V) and V.V B. Find the value of the constant B such that the vectors: u…

A: We can find the curl and divergence of vectors by using the formula The condition for the vectors to…

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Let u =j- 3k, v = - 9i + 3j – 3k, w = 3i -j+ k. Which vectors, if any are (a) perpendicular? (b)…

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Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: .b,č are three vectors such that a + b+ e = 0, lal = 5.6 = 3. = 8 then ä.b+ ans. -49 48 1/6

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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: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: Let u= -10i+4j- 4k, v= 5i-2j+2k, w=2j-5k. Which vectors, if any are (a) perpendicular? (b) Parallel?

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Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

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Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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Q: Find the measure of the angle between the two vectors. 1) u = (4, 9) v=(-3, -8) 2) u = (-8, 9) v =…

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Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

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Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

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Q: (a) Consider two vectors u = 3 and v = 5 in R4, Show that 5 7 7 i) u.v = v.u ii) d(u, v) > 0 [-31

A: Two vectors u and v is given in R4, and the vector is given as:

Q: Given the vectors u = -i-5j and v =-3i+2j, find u v

A: Given vectors are  u=-i-5j     and   v=-3i+2j

Q: Determine whether or not the given two vectors are parallel.u =〈4, 2, -6〉, v =〈2, -1, 3〉

A: To determine whether or not the given two vectors are parallel.u=4,2,-6 and v=2,-1,3 By definition,…

Q: The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j…

A: Use Cross product of vector

Q: 2) Let u=5i-j+k, v=j-5k and w=-15i +3j-3k. Which vectors, if any, are: a. Perpendicular? b.…

A: To find out the vectors which are parallel and perpendicular.

Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

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Q: 2. Determine the value of c, so the given vectors are perpendicular: u=[-4c, 3], v = [-1, 2]

A: L

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

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: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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Q: Find A:D,AAU ® let Ā = i+2j-K , B=-i+j+ K,itk> D=i+2j-K which vectors are: @ perpendiCular 6…

A: Please see the explanation below

Q: Show that the indicated diagonal ofthe parallelogram determined by vectors u and v bisects the…

A: The given parallelogram is   Here, we are given |u|=|v| So, u+v is the required diagonal

Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

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Q: Use the given vectors to compute u + v, u – v, and 2u u = (4, -3), v = (7, 9) u + v = u - v = 2u -…

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Q: State whether the vectors are parallel, orthogonal, or neither. 5) v = 2i + j, w =i- 2j 6) v = 2i +…

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Q: The distance between vectors v1 = (2, 1, -4) and v2 = (1, -1, -2) equals: Select one: O a. -2 O b. 3…

A: To find The distance between the two vectors v1=(2,1,-4) and v2=(1,-1,-2)

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

A: here, the given vectors, A =u+vB=u-v given that, they are orthogonal, that is, A·B=0u+v·u-v=0⋯⋯1

Q: Think of the letter X as four vectors starting from the center and pointing outward. Label the four…

A: Given 4 vector u,v,w,z. Need to provide information regarding cross product.

Q: 3. Find the angles between the vectors: a. u = 2i + j, b. u = 2i – 2j + k, v = 3i + 4k v = i + 2j –…

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

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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.