If u, v and w are mutually perpendicular vectors, which of the following would not be true? O a) v• (u - w) = 0 %3D O b) w• (v + ū) = 0

Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

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

A:

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

A: We can evaluate  the given problem as follows:

Q: given two vectors v m which are perpendicular. under which condition is V+W perpendicular to V-W?

A: Since vectors v and w are perpendicular so, their dot product is 0

Q: When the angle between vectors u and v is between 0° and 90°: || You can't tell O t • 0

A:

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: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Prove the stated property of distance between vectors. d(u, w) &lt;= d(u, v) + d(v, w) for all…

A: We have to prove the property of distance between vectors as,

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: 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: What is the angle measure between the vectors u = (-5, 8) and v = (3, 9)?

A:

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…

A:

Q: The angle between the vectors A = 17- 31+4 k and B= 5î -3ĵ+0 k, in term of cose is Answer:

A:

Q: What are the possible angles θ between two unit vectors e and f if ||e × f|| = 1/2 ?

A: The cross product of two vectors can be found by the formula a→×b→=a→b→sinθ The magnitude of the…

Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

A:

Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: Suppose that u and v are unit vectors in R°. If the angle between u and v is T/4, then what is the…

A: Given that vectors u and v are unit vectors and angle between vectors u and v is π4.  We know that…

Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: What is the angle e between the vectors u= and v= in R* ? (Express the answer to the nearest…

A: B

Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

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Q: The inner(dot) product of two vectors and with lengths a and b. is given by a-b = abcos(y+2 T) ,…

A: The statement is true. The given statement is true because , Given a→.b→=abcosγ+2π But, cos…

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

A:

Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

Q: The area of the parallelogram whose adjacent sides are the vectors u and v is a) Ju · v| c) Ju x v|…

A:

Q: A=\+2) -Kg B=-i+j+ K, Csitk, D= i+2j-K which vectors are: @ perpendicular parallel-

A:

Q: Find the area of the triangle with two sides given by the vectors a = i – j+ 4k, and b = 2i – 4j+1k

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: If u and v are orthogonal, what is the magnitude of u × v?

A: We define the cross product of any two vectors as :                            |u×v|=|u||v|sinθ…

Q: Verify the parallelogram law for vectors u and v in R": |u + v|l? + ||u – v||° = 2||u||? + 2||v||?

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Q: If r is equal to 300 mm, Find: 1.) Rectangular form of r in ft 2.) Unit vector of r

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Q: If u, and u2 are orthogonal unit vectors, and v = au, + bu2, find v•uq. = 'n.a v•u,

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Q: Let A and B be nonzero vectors and let C = ||B||A+ ||A||B . Show that the measure of the angle…

A:

Q: Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: given the vectors from R, (-5 0 3) belongs to span{v,, V2, V3}. Select one: O True O False

A:

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: Prove the stated property of distance between vectors.d(u, w) &lt; d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

Q: Find the measure of the angle between the two vectors. 24) u-(9,9) v-(-8,-5) V =

A:

Q: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

A:

Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: the angles between the vectors u = 2i - 2j+ k, v = 3i + 4k = O 84.2 O 40.2 O 48.2 80.3

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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: Find the value of a so that vectors U = ai + 12j and V = 31 + 9j are perpendicular. a =

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Q: Suppose that |u| = 6 and |v| = 9, and that u times v = -37. Find the angle θ between the vectors u…

A: Vector Question

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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