Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0 is the angle between vectors a and b, show that proją b proj, a = (a. b) cos²0

Q: Determine the angle between the given vectors. (а) а — 3і — 2ј, b %3 2i + 2j

A: a→=3i - 2jb→=2i + 2j

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction?…

A: Given: v=6,9 and point -6,-9 in the same direction

Q: Let ä = ( – 2, 0) and b = (2, – 5). %3D Find the angle between the vector, in degrees.

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Q: Find the angle between the two vectors and determine if theY are, or thogonai: ü=5i-33+2k ahd V=-i-…

A: We will use the formula: θ=cos-1u→·v→u→v→First we calculate:…

Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

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Q: Find u ⋅ v if u and v are unit vectors and the angle between u and v is π.

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Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

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: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

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

A: Hence the two vector u and v have same length.

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

A:

Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle 0 between the vectors v and w.…

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Q: Find the angle between vectors: a = 51-4j+2k and, b= 41+3)+2√5k

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Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: Consider the vectors u = (7,1,5, -5) and i = (3,4, c,0) in R*. a. Find the value of c that will make…

A: In this question, the concept of scalar products is applied. Given, u→=7,1,5,-5 and v→=3,4,c,0 in R4

Q: Find the angle between the vectors v and w v = (2, 1, 3)T , w = (6, 3, 9)T

A: We need to find the angle between the two vectors.

Q: Determine the value(s) of ? such that the vectors [5, ?, −8 ] and [3, ?, ?] are perpendicular.

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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: The angle between the vectors a=(2,6) and b=(3,-1) is Select one: O a. O b. 3 3. O d.

A: Angle between two vector  Vector a = 2i+6j Vector b= 3i-j

Q: Find all unit vectors perpendicular to (3,1,4) that make equal angles with j and k.

A: Here we have to find the all unit vectors perpendicular to (3,1,4) that make equal angles with j and…

Q: Find the angle between the vectors v and w v = (2,−3)T , w = (3, 2)T

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Q: * For the vectors v=16,8) and W=18,6), validate the Schwarz and Triangle mequaiity and fino the…

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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: Find the measure of the angle between the two vectors. 4) u =(-6, -2) v = (6,-6)

A: An angle between 2 vectors is defined as, cosθ=u→·v→|u→||v→|   Here given vectors are,…

Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: Find u * v if u and v are unit vectors and the angle between them is (2pi)/3

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Q: Find all unit vectors perpendicular to (3, 1, 4) that make equal angles withj and k.

A: Here we have to find the unit vector. The solution is following.

Q: Consider two vectors u, v, and is the angle between them, which of the following is false A. 00 if…

A: Given two vectors u→,v→ and θ is the angle between them

Q: Find the angle between the vectors u = (2, 5) amd v =

A: Given: There are two vectors: u=2,5v=4,-3 To determine: The angle between the given two vectors.…

Q: If U1 and U2 are orthogonal unit vectors and V = aU1 +b U2, find V.U.

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Q: .Let u and v be two vectors with u x= 2 and 7-5=-2 Find the angle 0 between u and i

A: cross product of the vectors:A⇀×B ⇀= A⇀B⇀sinθn^  (It's a vector quantity.)A⇀×B ⇀ =  A⇀B⇀sinθDot…

Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: If u is a unit vector find the dot product of vectors u and w

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Q: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

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: Consider the vectors u = (7,1,5, -5) and i = (3,4, c, 0) in R*. a. Find the value of c that will…

A: Given, The unit vector is in the same direction as u→=7,1,5,-5.

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

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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: 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: Find the angle between the vectors u and v if u (2,3,5) and v = : (1,–4,3) in (Ctrl) ►

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Q: Find the vector in v that has magnitude 8 and is in the opposite direction of (-3, –5, 1). v = help…

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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 angel between the vectors u and v if u=-4i+2j and v=3i+2j Round answer to two decimal…

A: Consider the dot product of two vectors.

Q: Find the vector in vl that has magnitude 8| and is in the opposite direction of (-3, –5, 1). v =||…

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

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