Find the initial point of the vector that is equivalent to u = (2, 2, 4) and whose terminal point is B(−2, −2, 3).

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: Find the unit vector in the same direction as the vector u = [8, –7].

A: When you divide a vector by its magnitude you get an unit vector along its direction.

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: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Find a vector ū that is parallel to the yz-plane and perpendicular to the vector i = (0, 2, 2).

A:

Q: Find a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2…

A:

Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

A:

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Find a unit vector u in the direction of the vector from P1(1, 0, 1) to P2(3, 2, 0).

A: Concept: Unit vector is a quantity which has a magnitude as 1and as well as direction, it is also…

Q: Find the terminal point of a vector of magnitude 5 that is parallel to the vector 1, 2, 3 and whose…

A: We will first find direction of vector using the magnitude and values of initial point and parallel…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1)

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

A:

Q: Express the vector v =12i -5j as the sum of a vector parallel to b = 3i +4j and a vector orthogonal…

A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

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: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

Q: Find the angle θ between the two vectors.u = (0, 4, 0, −1), v = (1, 1, 3, −3)

A:

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

A: The given points are: A=3,9,2B=-7,1,-4  Therefore, A→=3i+9j+2kB→=-7i+j-4k  To find the vector…

Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

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Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

A:

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

A:

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

A:

Q: Find a non-zero vector x perpendicular to the vectors  v= [-3]    And u = [-1]      [11]…

A:

Q: Let v be the vector from initial point P1 = (-8, 6), to terminal point P2 = (-2, 3). Write v in…

A: Let v be the vector from initial point P1-8,6, to terminal point P2-2,3.

Q: Find the position vector for the vector having initial point P and terminal point Q. P = (-2, -3, 1)…

A: Find a and b by subtracting the x and y values for the terminal point minus the initial point.

Q: what is the terminal point of a vector with initial point that Ar (-1,0is equivalent to u 3,4 O B3)…

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: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is

A:

Q: what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a…

A: A scalar is a real number. A scaler is a single, independent number.  A vector is a ordered…

Q: Find a unit vector in the direction of u = (5, 3, 2).

A: Given vector is u=(5,3,2) Find a unit vector

Q: Find the position vector for the vector v, whose initial point is (0, −2) and terminal point is (5,…

A:

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (0, 1, 3, -1) V…

A: In  the given problem we have to find the vector v with the given length and the same direction as…

Q: Find the magnitude of the resultant vector. (-25.6, 7.7)- (-11, -9.8) 1R

A: letA→=-25.6, 7.7 and B→=-11,-9.8

Q: Express the vector x as a linear combination of u,, u2, and uz. – 2 3 - 2 ,x = 0 u2 = 5 u3 = – 4 u1…

A: Given u1=-201, u2=356, u3=-26-4 and x=-99-38

Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

A:

Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: Find the vector equation for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

A:

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Find the orthogonal projection of the vector a (-9,-8, 7) in the direction of the (-3,-5,-2). vector…

A:

Q: Find two linearly independent vectors perpendicular to the vector i = |3

A: to find linearly independent vector perpendicular to vector v→=139 solution let X=x1x2x3 as we know,…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 4y – 3x +3z = -2 and z…

A: Answer

Q: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry