Find all values of h such that the vectors (a,, a,, a‚} span R°, where a a2 = 14

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

Q: Find an equation of the plane that passes through the point (0, 0, 0) and is perpendicular to the…

A: The direction ratio of n = −3i + 2k is (-3,0,2) Given that that plane is perpendicular to n = −3i +…

Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

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Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

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Q: Find a unit vector that has the same direction as the given vector. 4i - j+ 8k

A: Unit vector means the vector whose magnitude is equal to one. So to find the unit vector in the…

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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Q: Find a unit vector in the xy-plane that is orthogonal to

A: Here given vector as a=123 Consider a vector as b=25-150 Now find the dot product of vector b to…

Q: Find the unit vector orthogonal to the plane through the points P ( 12, 3, -4 ), Q (-1, -2, 2), and…

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Q: Find vector V such that the vector has a length of 16 and makes an angle of n/3 with the x-axis.

A: Given problem:- Find vector V such that the vector has a length of 16 and makes an angle of π/3 with…

Q: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

A: WE know that equation of line through (x1,y1,z1) and parallel to vector ai+bj+ck is

Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

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Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Consider the vectors u = ⟨cos , sin , 0⟩ and v = ⟨cos , sin , 0⟩, where > . Find the dot product…

A: Consider the given vector u→=cosA,sinA,0 and v→=cosB,sinB,0

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

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: At what value of k are these vectors collinear?

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Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Find the angle 0 between the vectors. 5T u-(cos , sin S), v-(cos, sin 4) = 4 4 3

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Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: ind The normal vector to The vectou zi-3;+ 4 K so/ There is 0 numberof vectors.lin spaci).

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Q: Select any 4 vectors in Calculate R" of your choice. V,'s, applying Eq A on these vectors.

A: There is a misprint in the question given. In the equation (A) given in the question, the summation…

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

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Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

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

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Q: ': Find all unit vectors parallel to the and perpendicular to the plane vector V = 5i -j + 2k

A: Here we find all unit vector parallel to the yz plane and perpendicular to the vectorv→=5i∧-j∧+2k∧

Q: Find a unit vector perpendicular to i-j and to i +k and with a positive k component.

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Q: Qy: In VĘ CR) find all vectors which are orthegonal to u=(1,-2, 3) uut corath

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Q: A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

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Q: Find the normal unit vector perpendicular on à and B for A = 2i+3j-k and B=-j+2k %3D

A: To find the normal unit vector perpendicular to A and B

Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

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

Q: Parametrize the line that passes through the point (1, 2, 3) rallel to the vector V = -3i +7k .

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

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Q: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

Q: Find a unit vector in the xy plane that is orthogonal 2 to 4 6

A: We have to find the unit vector.

Q: Find the values of x such that the angle between the vectors ⟨2, 1, −1⟩ and ⟨1, x, 0⟩ is 45 . (Pls…

A: The angle between the vectors ⟨2, 1, −1⟩ and ⟨1, x, 0⟩ is 45 degrees. We need to find the value of x