d a vector orthogonal to both u and v.

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: Let v be the vector from initial point P1 = (3, -1) to terminal point P2 = (-2, 5).Write v in terms…

A: Given the points P1=3,-1 and P2=-2,5.   The vector is, v=P1P2→=-2-3,5--1=-5,6

Q: s opposite direction to the vector u = .

A:

Q: ind a unit vector orthogonal to bothu and v. u = (-8, 7, -2) v = (-1, 1, 0)

A:

Q: Find a unit vector orthogonal to both u and v. u = 31 - 2j + 5k V = + 10 2

A:

Q: Let v be the vector from initial point P1 = (-1, 3) to terminal point P2 = (2, 7). Write v in terms…

A: Given : the two points are given as P1=-1,3 and P2=2,7 To find: a vector v from initial point P1 to…

Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

A:

Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=<4, -5, 7> onto the vector…

Q: What is the resultant of vectors a and b? ( A ) GL B

A:

Q: Find a unit vector orthogonal to both u and v. u = -5i – 3j - 2k | V =

A: Two vectors A and B are said to be orthogonal to each other if and only if their dot product is zero…

Q: 2; Find a vector of magnitude 3 in the direction v = (0, 3, –4)

A: The given direction is 0,3,-4.

Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

A:

Q: Find u + v, u − v, and 2u − 3v. Then sketch the resultant vector. u = 4,3    , v = -3, 0

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Q: Express the vector in the form (a, b). 1(i + j) ji + jl

A:

Q: 2 nogonal to the vector

A: The coordinates of point M is 1,1,0 . The orthogonal vector to M is 200. The equation of the plane…

Q: 2. Find the unit vector in the direction of

A:

Q: Find vector c = 3u – v, if u = and v =.

A: Given u = 2i - 7j + 3k and             v = 0i + 4j -  k = 4j - k Now vector c = 3u - (1/2)v c = 3(2i…

Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: Let v be the vector from initial point P1 = (2, -1) to terminal point P2 = (5, -3). Write v in terms…

A: Given that v is the vector that has initial point P1 = (2, -1) to terminal point P2 = (5, -3).  we…

Q: Find a non-zero vector i perpendicular to the vector i

A: See the attachment

Q: Find a unit vector u with the same direction as vector v =

A:

Q: Find the vector of length v7 in the direction of AB + AC

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Q: Find the unit vector u in the di rection of the vector v=2(2, 1, 2).

A:

Q: Find a unit vector orthogonal to both u and v. u = i + 2j v = i+ 3k

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Q: and the unit vector along the direction of u.

A:

Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

A:

Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

A:

Q: Let u=(-2, 0, 1) and v-(-7, -1, 3). Find the value of the j-component in the vector 5u-6v

A: The given vectors are:u=-2,0,1 and v=-7,-1,3First we find the vectors 5u and 6v.

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

A:

Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Find a non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: Find the magnitude of the vector u =

A:

Q: Describe all vectors v that are orthogonal to u

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Q: Find the unit vector u in the direction of the vector v=4(2, 1, 2).

A:

Q: Let v be the vector from initial point P1 = (-3, 0) to terminal point P2 = (-2, -2). Write v in…

A: Solution:- we have to find vector v in which  initial point P1 = (-3, 0) to terminal point P2 = (-2,…

Q: B. Find a vector has length 10 in the direction of vector V=.

A:

Q: Find a non-zero vector u perpendicular to the vector u =

A: If  A non zero vector is perpendicular to anather vector then their dot product is equal to zero.

Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: Find the unit vector u in the direction of v. Verify that u| =1. 12. (1,–6)

A: solution is given below..

Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

A:

Q: Let v be the vector from initial point P1 = (4, -5) to terminal point P2 = (4, 3). Write v in terms…

A:

Q: What is the vector j?

A: We have to tell what is vector j   it is also written as j→

Q: Let u and v = .A vector orthogonal to both ú and v is

A:

Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…

Q: Let vector u = and vector v . Find the magnitude of 3u-4v. Round to one decimal place.

A: Let vector u= <3, 4> and vector v = <6, 7> then find the magnitude of vector 3u-4v.