Consider the points below. Р(3, -2, 5), Q(-1, -2, 1), R(2, 1, -3) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. 6i + 2j – 2k (b) Find the area of the triangle PQR.

Q: B) Given the vectors u = 7i+ 2j -k, v = 2i-3j-6k. Find the projection of %3D u onto v.

A: Using projection vector formula.

Q: Find equations for the planes The plane through A(1, -2, 1) perpendicular to the vector from the…

A: The normal vector of the plane is given by A(1,-2,1)  The point of passing is (0,0,0). The equation…

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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Q: Given the vectors in parts a) and b), determine whether u, v, and w lie in the same plane when…

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Q: The surface of a hill is modeled by z = 100 – 3x? – 4y². When a group of hikers reach the point (1,…

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Q: Which of the following vectors is perpendicular to the plane 2x - 3y + 5z + 7 = 0?   a. [-3, 2,…

A: Given: The equation of the plane is  2x - 3y + 5z + 7 = 0   To determine: The vector which is…

Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: Which of the following vectors is orthogonal to the plane 3(x - 7) + (y + 8) - 5z = 15? O O O

A: Given equations of plane 3(x-7) +(y+8)-5z=15this is an equation of the form a(x-x1)+b(y-y1)+…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: point = (3,5,-7)n=0 i +1 j + 0 kCartesian equation of plane is Ax+By+Cz+D=0(A,B,C)=( 0,1,0)(x,y,z) =…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Suppose we have the triangle with vertices P(1,5, 1), Q(-4, 10, –1), and R(6, –3, -1). Answer the…

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Q: f(r.y2)4ry t and u is the unit vector in the direction of (4, 2,-5), men the drectional denvative at…

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Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1, √5). Find the coordinates of the vector QS…

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Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

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A: The dot product of two vectors u→, v→ is calculated using the formula: u→·v→=u→v→cosθ, where θ is…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given: (2,3,-6) Perpendicular to j vector

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Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

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Q: Given a vector à = 3a, + 2a, – 6as , determine the vector component of à tangential to the cone. O…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

Q: Find the unite vector perpendicular to the plane 4x + 2y +4z = -7

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Q: 3. For the vectors b= (2, -1, -2) and a = (0, 4, –3) (a) Compute the projection of vector b onto the…

A: Consider the equation

Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out b) e1-e3

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Q: Let u = (2, – 4) and v =(-4,2). Find the component form and magnitude (length) of the vector 2u -…

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Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: Consider the vectors u -1 and w 6 -2 a. Compute u · (20+ w). b. Is ú in the plane spanned by u and…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: 2. Given the points P(-1,3, 1), Q(0,5, 2), R(4,3, –1), (a) Find a nonzero vector orthogonal to the…

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Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

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Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: Find the equation of the plane passes through the point P(4,2,1) and perpendicular to the vector…

A: Equation of the plane passing through point P(x0,y0,z0) on the plane and perpendicular to the vector…

Q: Q3 find 1)angle between two vector. 2)projection of vector A&B. A = 2i + 2j - K B = 4i-6j + 4k

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Q: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: Find the component form of the vector v given ||v|| 12 following the direction of u (3, –5) %3D

A: The vector v in direction of u can be found  blew step.

Q: Given a vector Á = 3a, + 2a, + 6as , determine the vector component of Á perpendicular to the…

A: Topic:- vector

Q: Q1A) The vectors A = 3i + j + 4k, B = 2i - 3j - k, find vector normal to A and In plane of A and, B.

A: Solution is given below:

Q: Given that a = (-10,9,13) and b = (14,–6,12), а. i) ii) compute the dot product. find a vector…

A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

Q: Consider the vectors u = (7,1,5, -5) and i = (3,4, c, 0) in R*. a. Find the value of c that will…

A: Given, The unit vector is in the same direction as u→=7,1,5,-5.

Q: Let / be the line through the point with coordinates (1,0,0) in the direction of the vector -2 .…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: )P=(3,2,1), then the parametric equation of the line is :   a.

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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

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Q: Find an equation of the plane passing through the given point and perpendicular to the given vector.…

A: Equation of a plane perpendicular to a, b, c and passing through x0, y0, z0 is, ax-x0+by-y0+cz-z0=0

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

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