a linear combination of the vectors Can we express the vector a = (2, – 5, 3) as e = (1, 1, 1), ez = (1, 2, 3) and e, = (2, – 1, 1) in R'(R).

Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: The vector v = ⟨−1, 3⟩ and its Initial point: (4, 2). Find the terminal point.

A: Given: To Find: Terminal Point   Concept:

Q: The vector (-1, 5, 3) is orthogonal to vector : Select one: О а. (0, 1, -2) O b. (-1, 1, -2) О с.…

A: Two non-zero vectors are orthogonal to each other if their dot product is equal to zero.

Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

A:

Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: find a vector parametrization for the line with thegiven description.Passes through P = (1, 2, −8),…

A: Find a vector parametrization for the line with the given description. Passes through P = (1, 2,…

Q: (a) Using Gaussian elimination, find a vector v such that

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one.…

Q: Pls help ASAP

A: It is vector problem

Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

A:

Q: Obtain a vector orthonormal to the vectors i−j  and (1, 0, 1)

A:

Q: Find the terminal point of a vector v = with an initial point P(0, 6, 2).

A:

Q: find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: 18 as a linear combination of a and y Express the vector v y.

A:

Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

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 the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

A:

Q: The position vector of a moving particle in space at time t is given by the vector function r (t) =…

A: position vector of particle in space r→(t)=12(5-t)2i→+(2t-1)j→+43(5-t)32k→

Q: 2. Express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of…

A: position vectors

Q: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: A. If x and y are orthonormal vectors, then find the value of x+ yll- x-yll

A:

Q: Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

A: The given vectors are u=(0,1,1) & v=(1,0,1).

Q: Find two unit vectors orthogonal to both u→=⟨3,4,1⟩ and v→=⟨0,3,3⟩.

A:

Q: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…

A:

Q: Find the coordinate vector of v relative to the basis S = {v,, V2, V3} for R³. (b) v = (5, –12, 3);…

A:

Q: Q2: Determined the component of the vectors at each point…

A:

Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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: If the vector v has initial point P, what is its terminal point? v = (0, 0, 3), P(0, 3, -3) (x, y,…

A: Let's find.

Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

A:

Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

A:

Q: Determine the vectors axe linear yy independent -3 2. 8. O ON

A: For linearly dependent determinant  of matrix is zero D=0

Q: (8) Find a vector parameterization of the line r(t) which passes through the point P = (1,2, –8)…

A:

Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: Consider the vector v = 2t2 + 1 1 (2t, 2t², 1) . The derivative of v with respect to t is (2 – 4t²,…

A: Using the quotient rule of differentiation, it can be written as follows. ddxxy=ydxdy-xy2

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

A:

Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A:

Q: Find a unit vector orthogonal to both u and v. u = (-4, 5, -2) v = (-1, 1, 0)

A: The vector which is orthogonal to both u and v is defined as u×vu×v. Here, u=-4,5,-2 and v=-1,1,0.…

Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

A:

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

A:

Q: Find a vector ~v ∈ R^3 such that ~v is orthogonal to the vectors (2, 3, −1) and (1, −2, 3) and ~v ·…

A:

Q: 1. The vector in the opposite direction to u = (-2, 2) and of half its length is 2. The vector of…

A: Given vector is u→=-2i+2j To find the vector in opposite direction and half its length.

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0). LO î + 27 (F (smaller i-value) î…

A: Use the given information.

Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

A:

Q: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

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 the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

A: