Consider the points below. P(0, –3, 0), Q(6, 1, –2), R(6, 4, 1) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR.

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A: To Find an equation of the plane that passes through the given point (1, 3, -7). First, convert the…

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

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Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. -2u

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Q: ii) Find the dot product of the vector a in part (i) with the displacement vector AB such that…

A: Given that  Following vectors  To find the dot product

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Q: 3. Express the following vectors in Cartesian (component) form. Z a) f has magnitude 20 and…

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

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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…

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: Find the vectors T, N, and B at the given point. r(t) = re) - (2. 20,0). (1, - 3 -1) T = N = B =

A: Here we have to find,  Unit tangent vector T→(t)=? Unit normal vector N→(t)=? Unit Binormal vector…

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Q: Given the vectors: A = 7+7+ k and B= 47+ 27+ k Find the vector projection of A onto B: Proj. _, A

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Q: Consider the points A (10, 9) and B (0, – 7). Find the vector AB. АВ

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Q: Consider the vectors u = (2,0) and v = (-4,4). Sketch the vectors, find the angle between the…

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Q: Let a =)33) A) Find the eavution of the Plane which has a a nomal vector t conthins Point 3,3) Find…

A: To solve this problem we use here the definition of a plane passing through a given point and…

Q: Q3. Prove that (only one): a-dy is a unit vector? a- %3! b- L = 6a, - 3a, + 2a, and M = 3a, + 2a, -…

A: Topic- Vector

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z 2x2 + y and…

A: z=2x2+y2  & x=ey We can see that y can be represented in terms of x.

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: (c) Find the vector equation of the line of intersection of the planes x-2y+z=0 and x+y=z= 1.

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

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Q: E. Find an equation of the plane passing through the point (6, 3, 5) and containing the line of…

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Q: What is the y component of vector a? Only provide an integer answer such as 0, 5, 10, etc. 10 10…

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Q: Let u = (-3,4) and v = (2, –5). Find (a) the component form of the vector 3u – 4v and (b) its…

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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: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two 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: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find the vectors T, N, and B at the given point. r(t) =< t2 ,(2/3)t3 ,t>   ,  (4,16/3 ,2)

A: Consider the given vector function.

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Q: Qe A Find the Vector 5 unit length in the direction of vector perpendicular to the lane which passes…

A: We have to find the normal vector first.

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: Find the vectors T, N, and B at the given point. r(t)= (t2)i+(2/3(t3)) j + (t)k, (1,-2/3,-1)

A: Given, rt=t2i+23t3j+tk Point - 1, -23, -1 So, t=-1 Formula Used: Tt=r'tr'tNt=T'tT'tBt=Tt×Nt Quotient…

Q: Find the vectors T, N, and B at the given point. r(t) ) =(2², ²32²³, t), (4,- 15, -2) N = B =

A: This question can be solved by applying the formula of T,N,B