The moment vector of the force p = [2, 1, -3] about Q:(-2, 1, 0) acting on a line through A:(1, 2, 2) is O A [5, 13, -1] O B. [-5, - 13, 1] Oc [-5, 13, 1] O D. None of these

Q: 2. Let f(x,y) = t Find the direction of a unit vector so that Daf is minimal at point (0, 1). %3D 3…

A: To find the direction of a unit vector u so that the directional derivative of f at point (0,1) in…

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: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

A:

Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

A:

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

Q: P that is orthogonal to the vector AB. . B e distance from the point P(-3,1,9) В(-2,3, —4).

A:

Q: Suppose that u, v are vectors in R3 , u · v = 1, ||v|| = 1, the angle between u and v is π/3, and u…

A: The detailed solution is as follows below:

Q: Pls help ASAP

A: It is vector problem

Q: The moment vector of the force p=[1,-2, 3] about Q (1, -2, 1) acting on a line through A:(2, 1, 0)…

A: Known fact: The moment vector m of a force F about Q acting on the line passing through the point A…

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: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

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

A:

Q: Expreas the unit vector dirccted toward the point (0,0, A) from arbitrary point in the plane --2. an

A: In this question, we have to find the unit vector toward the given point from the given plane the…

Q: Find a vector of length 5 in the direction of (2, 1). O A (V2,1) В. (2/5, V5) OC. (10, 5) O D. (2,…

A: see 2nd step.

Q: A. Given force (F = F1 – F2), transform the force vector F to cylindrical coordinate system at point…

A: The given vectors: F1=25ax-17ay+12azF2=15ax+9ay+6az

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y? = 8 and y? + 22 = 8…

A:

Q: The moment vector m the force p [1, 2, 3] about the point Q(1, 2, 3) acting along the line passing…

A: The moment of force is given by m⇀=r⇀×F⇀ where F⇀ is the force vector and r⇀ is the radius vector.…

Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

A:

Q: Find the vector ū which satisfies the given conditions. i =, Ju| = 2 , ū and i have opposite…

A: The unit vector,  , in the direction of the vector is calculated as follows.

Q: The moment vector of the force p = [1, -2, 3] about Q (1, -2, 1) acting on a line through A:(2, 1,…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: A line l passes through the point P(2,4, 3) and is parallel to the vector (3, 2, –3). | At what…

A: Proceed as shown below

Q: Find the unit vector u in the di rection of the vector v=4 (2, 1, 2) 1 U = OA 1 U = 1 Oc. 12 OD. 1 u…

A:

Q: -x + 6y + 2z = 6 1. -x + 3y + z = 7 2 Find the normal vector, n,, to -x + 6y + 2z = 6. n = 1 Find…

A:

Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

A:

Q: Suppose that ∇ƒ(x, y, z) is always parallel to the position vector x i + y j + z k. Show that ƒ(0,…

A:

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: The moment vector of the force p=[1, -2, 3] about Q (1, -2, 1) acting on a line through A (2, 1, 0)…

A: This question is related to vector.

Q: The moment vector of the force p= [2, 1, -3] about Q:(-2, 1, 0) acting on a line through A:(1, 2, 2)…

A:

Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: The vector w is a unit vector, and the vector i is any non-zero vector. If z = (x · W)w and ỹ = i –…

A: Use the property of dot product and associative and distribute property to solve the problem.

Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

A:

Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: Let vectors u=[1,0,-1] and v=[-2,1,2].Find the vector w that is orthogonal to both u and v

A: The given vector is u=[1,0,-1] and v=[-2,1,2]

Q: A force F of 6 units acts through the point P = (2, 3, 1) in the direction of the vector (4, 1, 2).…

A: the moment formula M= r×F here r = vector PQ r =  OQ→-OP→ = (-1,-1,0) And the F vector is 6 times…

Q: If a force F-2i -3j+k acts at the point (1,5,2), then the torque about z-axis is 13k 13 -13

A:

Q: Q3. Prove that (only one): ax-V3ay a- is a unit vector? b- A = 6ax – 3a, + 2a, and B = 3ax + 2a,y –…

A: Given two statements . We need to prove only one out of that  So, here we will prove first statement…

Q: For any vectorV and unit vector U parallel to V , then D-

A:

Q: Q3) Find the vector ž, which is perpendicular to vectors ã = (2,3, –1) and b = (1,–2,3) and…

A:

Q: Using the vectors from the previous problem, find the projection ul of v onto the vector u and find…

A: We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product…

Q: The moment vector of the force p=[1, -2, 3]about Q (1, -2, 1) acting on a line through A:(2, 1, 0)…

A: To calculate the moment vector (m) use the formula m=r×p,where r is the position verctor.Here the…

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: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Q: The moment vector of the force p=[1, -2, 3]about Q (1, -2, 1) acting on a line through A (2, 1, 0)…

A:

Q: Find the work done by the force F=(1,3) in moving an object from A(4, 5) to B(-2, 8).

A: Explanation of the answer is as follows