Find the equation of the plane with normal vector n = (8, 7, 3) passing through the point (4,,9) in scalar form. (Use symbolic notation and fractions where needed.) the equation:

Q: Find the vector parametric equations for the line. in the direction of the vector – i+ 5j-3 k and…

A: equation of line in vector parametric form

Q: Find a vector equation for the plane that contains the points P, Q and R Find a scalar equation for…

A: Given points: P(2,1,1),Q(0,4,1),R(−2,1,4) and S(1,5,−4) Equation of a plane in cartesian form…

Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

A:

Q: Find a vector equation for the line segment from (2, -4, 6) to (5, 5, 5). (Use the parameter t.)…

A: a→=2i-4j+6kb→=5i+5j+5kn→=b→-a→=3i+9j-k

Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: Find the component form and magnitude of the vector v. Initial Point Terminal Point (-2, 15) (-26,…

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Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(-4, 8, 0),…

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Q: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…

A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane

Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)…

A: We will find an equation of the plane through the point (8,2,3) and perpendicular to the given…

Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: Find a vector equation for the line through the point (-3, –1, 8) perpendicular to the vectors ū =…

A: Vector equation of the line passing through point (a,b,c) and perpendicular to vectors u→ and v→ is…

Q: Find an equation of the plane that passes through the point P(-7,–5,5) and has the vector n = (-1,4,…

A: Given : Point P(-7,-5,5) and a normal vector n=<-1,4,2>   To Find : Equation of the plane that…

Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…

A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…

Q: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

A: WE know that equation of line through (x1,y1,z1) and parallel to vector ai+bj+ck is

Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

A:

Q: Find the equation for the plane through the point Po = (2,2,7) and normal to the vector n= 8i + 3j +…

A: Equation of plane passing through point P(x0,y0,z0) and normal to vector n=ai+bj+ck is given by:…

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Write the equation of the plane with normal vector n passing through point Po in the scalar form ax…

A: Topic = Vector

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Write the scalar equation of the plane with normal vector = [1, 2, 1)] and passing through the point…

A: here normal vector is  and the given point is

Q: Write a scalar equation of each plane, Given its vector equation [x, y, z] = [7, -3, 4]+s [1, -2,…

A:

Q: Write an equation of the plane with normal vector n (7,5, -4) passing through the point (1, −5, 1)…

A: Given; n=<7,-5,4> Point (1,-5,1).

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

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

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…

Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: Write the equation of the plane with normal vector n=5j passing through the point (2,10,9) in scalar…

A: Give normal vector is:

Q: Find an equation of the plane that passes through the point Po(0,2, – 2) with a normal vector n =…

A: Find an equation of the plane that passes through the point p0 (0,2,-2)with a normal vector…

Q: Find:   a) the parametric equation of the line determined by points A(1,0,2) and B(2.2.1). b) the…

A:

Q: Let u=(-2, 0, 1) and v-(-7, -1, 3). Find the value of the j-component in the vector 5u-6v

A: The given vectors are:u=-2,0,1 and v=-7,-1,3First we find the vectors 5u and 6v.

Q: Find the vector parametric equations for the line. in the direction of the vector 4 i – 3j- 3k and…

A: Equation of the line passing through a given point a,b,c and in a given direction l i+m j+n k is…

Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: find the component form of the vector. The vector 2 units long in the direction 4i - j

A: Given vector is u = 4i – j. So, the unit vector in the direction of the given vector is

Q: Write an equation of the plane with normal vector n (7,5, −4) passing through the point (1, −5, 1)…

A:

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

Q: find the component form of the vector. The unit vector obtained by rotating the vector {1, 0}135°…

A: The unit vector obtained by rotating the vector {1, 0}135° counterclockwise about the origin.

Q: Find an equation of the plane. The plane through the point (4, 8, 6) and with normal vector 7i + j -…

A: Given, The plane passing through the point (4,8,6) with the normal vector 7i+j-k We know that, The…

Q: snip1

A: The given point is, P=1,2,-1 which is parallel to the vector d=5-13. The objective is to find the…

Q: Find the component form and magnitude of the vector v. Initial Point Terminal Point (-2, 3) (11,…

A: Given for a vector v,Initial point:(-2,3)Terminal point:(11,-19)

Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: write the equation of the plane passing through P with normal vector n in (a) normal form and (b)…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, −1,…

A: Find a  vector equation and parametric equation for the line joining P and QP (1,-1,5) and Q (5,2,1)

Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

A:

Q: Write the scalar equation of the plane with normal vector * - [3, 4, – 1] and passing through the…

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Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

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Q: Find a vector equation and parametric equations in t for the line through the point and parallel to…

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Q: Find an equation of the plane that passes through the point P(-7,-2,5) and has the vector n = (-7,4,…

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