Evaluation the distance between Linel and Line2, where linel through points Q(1,0,-1) and S(-1,1,0) and the line2 through P(3,1,-1) and N(4,5,-2) and find the vector perpendicular to both lines:

Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

A: Given problem:- Find two vectors in opposite directions that are orthogonal to the vector u. (The…

Q: Cross products from the definition Sketch the following vectors u and v. Then compute |u × v| and…

A: Given : u=0,-2,0           v=0,1,0Find : Cross  product of u and v  u x V         Sketch the graph…

Q: Parameterize the plane that contains the three points (-2,-2,-2), (-12, 2, 12), and (0, 35, 30).…

A: To find the parametric equation of a plane containing three points (-2,-2,-2,), (-12,2,12) &…

Q: Using dot product find cos for the vectors u = (1, -3, 4) and v = (3,4, 7).

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Q: (B) Find a unit vector u with positive first coordinate that is parallel to both planes. i+ j+ k (C)…

A: The equation of line of intersection is given as follows :

Q: Use a software program or a graphing utility with vector capabilities to find the lengths of u and…

A: Given: u=0,14,13 , v=2,12,23

Q: Let v be the vector from initial point P, to terminal point P2. Write v in terms of i and j. P, =…

A: Now we will find the V using the formula  V = ( X2 - X1) i + ( Y2 - Y1) j

Q: (a) Find a nonzero vector orthogonal to the plane through the points P(0,- 2, 0), Q(4, 1, – 2), and…

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Q: b) Consider the vectors u = (2c, 2, −4), v=(c, c, 3)and w = (-1, 2, 3). Find the value(s) of…

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Q: Sketch the vector w on the grid on the right and label its coordinates. Vectors and + w are…

A: First write this in vector form then put this on the graph.

Q: Consider vectors u and v. Find unit vector w in the direction of the cross product vector u x v.…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line.…

A: Given  (x-3)9=(y+6)4=z+7

Q: : Triangle with points P(1,-1,2), Q(2,0,-1) and R(0,2,1), find: 1. Area of the triangle. 2. a unit…

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Q: Perpendicular vectors Show that two nonzero vectors u = (u, uz) and v = (Vị, v2) are perpendicular…

A: we have to show that two non zero vectors u=u1,u2 and v=v1,v2 are perpendicular to each other if…

Q: Find vector, para metric and symmetric equations of the line contalning the point P and parallel to…

A: P=p0+tv is the equation of vector.

Q: Vector component of V and w are as follows. Find the direction of the resultant vector. v = (13.5,…

A: The resultant vector is the sum of two vectors.

Q: a. Find the area of the triangle determined by the points P, Q,and R.b. Find a unit vector…

A: Calculate the area of the triangle with vertices P1,1,1, Q2,1,3, R3,-1,1.

Q: ecimal places.) u- (3,) v- (0,) (a) the norms of u and v ||u| - ||v || = (b) a unit vector in the…

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Q: a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) find the area…

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Q: Use vectors u= (-4,1) , v= (5,-2), and w= (0,6) to perform the indicated operation. Then determine…

A: The given vectors are: u=-4, 1v=5, -2w=0, 6

Q: The directed line segment from the point A to the point B in the Cartesian plane is the vector 1/2

A: We have to check given statement is true or false.

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

A: Three points are given, We have to find the equation of the plane contains the given three points.…

Q: Test tor the unit vector, orthogonality (1,-1,0,0) ū (-1,7,2,0)

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Q: () - (두루)- U = V = 3, (a) the norms of u and v |lu|| %3D |||| (b) a unit vector in the direction of…

A: The norm or length of a vector u=x,y,z is given by  u=x2+y2+z2. The unit vector in the direction of…

Q: Determine whethere the following statement is true or false. Explain. In the coordinate​ plane, the…

A: The angle of a vector is measured from the positive x-axis in the clockwise direction. The base of…

Q: Consider vectors u and v. Find unit vector w in the direction of the cross product vector u x v.…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line.   x − 1 4 =  y +…

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Q: Determine whether or not the two vectors u = (-2, –4,9) and v = (-4, –7, 18) are parallel. The…

A: Given query is to find vectors are parallel or not.

Q: Evaluation the distance between Linel and Line2, where linel through points Q(1,0,-1) and S(-1,1,0)…

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Q: (a) Determine the vector equation and the Cartesian equation of the plane B passin by the points…

A: This is a problem of vector calculus.

Q: Find the cross product a x b where a (-2, 2, 0) and b = (-4, 1, –1). %3D ахь- Find the cross product…

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Q: (3.) The distance of two vectors x and y, dist(x, y) =|| x-y ||= / (x – y, x – y). (a) Find dist(r,…

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Q: Find a unit vector in the direction of vector v = ⟨−2, 3⟩

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Q: Find the unit vectors u and uz in the directions of v = (1,3) and w = Find unit vectors U, and U2…

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Q: v=(-5.8,-3) ∈ R3 vector U={u1 = (1,-2,3), u2 =(-2,4,-1), u3=(2,-2,-3)} Find the coordinate vectors…

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Q: How do you find the vector that goes from a point A to another point B ? O You find the cross…

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Q: Evaluation the distance between Line1 and Line2, where line1 through points Q(1,0,-1) and S(-1,1,0)…

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

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Q: 4. Geometry: Given a line 2r + y = 2 in the two-dimensional plane, • If a given point (a, B)…

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Q: a. Find the area of the triangle determined by the points P, Q,and R.b. Find a unit vector…

A: Given that, P(1,-1,2) Q(2,0,-1) and R(0,2,1)   (a)   Area of Traingle PQR=12PQ→ x PR→We have PQ→…

Q: SEvaluation of JA - 2B| through define length of the vector |A| equal to and length of vector B|…

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Q: Q2: Find the vector and unit vector (u) in the direction of the vector P2 (-3,0,6) to P1 = (4, 6, –…

A: We have to find the vector and the unit vector(u) in the direction of the vector P2=(-3, 0, 6) to…

Q: Q.2B) Evaluation of |A – 2B| through define length of the vector JA| equal to and length of vector…

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Q: (3.) The distance of two vectors r and y, dist(r, y) =|| x–y ||= /(r – y, x – y). (a) Find dist(r,…

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Q: Esing the method Dot vectors product, find the equation in xy plane through the nt (3, 5) and…

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Q: Decompose v into two vectors, v, and v,, where v, is parallel to w and v, is orthogonal to w. v=…

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Q: the point P on the line and a vector v parallel to the line. x = 7t, y = 8 − t, z = 3 + 2t

A: By comparing standard parametric equation of a line with given line , we can easily find the point…

Q: Vector v1=[1, 1, 2]T, vector v2=[0, 1, 1]T, vector v3=[-1, 2, 0]T Transformation f : R3 -> R3 is…

A: Given vectors are v1=112, v2=001, v3=-120 Transformation is f:R3→R3 as follow f(v1)=-963T,…

Q: Which vector gives the direction vector of a line given by vector v = (-3,-5, 1) + t(7,2,3)

A: Let us consider the vector form a line r→=a→+tb→ Here, a→ is a position vector and, b→ is a…

Q: 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the given a and b.…

A: 2) Given vectors are a) a=1,2,3 and b=5,-1,-1 b) a=1,2,3 and b=4,8,12 c) a=1,2,3 and b=2,4,3