Find a vector equation and parametric equations for the line. (Use the parameter t.) the line through the point (9, 4, 1) and perpendicular to the plane 4x – 4y + 4z = 1 r(t) = (x(t), y(t), z(t)

Q: (A) Find the parametric equations for the line through the point P = (-4, -3, -5) that is…

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Q: Find a vector parametric equation r(t)|for the line through the points P = (-3, –2)|and Q = (-5,…

A: According to the problem, we have

Q: A line initiated from (1,0,2) and parallel to a vector 2i + j what is the parametric equation of the…

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Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

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Q: (A) Find the parametric equations for the line through the point P = (-5, 0, -3) that is…

A: Equation of line.

Q: Find the vector equation that represents the curve of intersection of the cylinder x² +y² = 4 and…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

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Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

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Q: Consider the line perpendicular to the surface z = x2 + y at the point where x = 1 and y = -1. Find…

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

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Q: 3+z Given the points R (1, -1, -3), the vector v = and the line d: ¯x+¹=1+y= 3 2 3. Calculate the…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, –1, 7),…

A: Please refer the attached image for complete solution.     Please refer the attached image for…

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, 0, 1),…

A: Given points are; P(1,0,1) ,Q(4,2,1).

Q: (1 point) Given a the vector equation r(t) = (4 + 4t)i + (1 + 1t)j + (1 + 4t)k, rewrite this in…

A: See below the answer

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) and (5,2,4),…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, -1, 6),…

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Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2 + 3t…

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Q: Find the vector and parametric equations for the line through the point P = (-4, –4, 5) and the…

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Q: Find the vector and parametric equations for the line through the point P(1, 1, -3) and orthogonal…

A: Given: Point= (1, 1, -3) Orthogonal to plane: 3y-4x+2z=3 The direction vector for this line is v=…

Q: a) Find the scalar parametric equation and vector equation (r = c + ta) of the straight line z+5 x –…

A: We have to find

Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: SOLUTION-

Q: Find the vector and parametric equations for the line through the point P(-2, 4, -3) and parallel to…

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Q: 1. Given the points P= (2,-4,-1) and Q=(5,-4, 2) in space. A) Find the parametric equations of the…

A: 1. A> we will find the parametric equation of the line using  two points  B> EXPRESS the…

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

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Q: Find both the vector equation and the parametric equations of the line through (0,0,4) in the…

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Q: Q2 a) Find the parametric equation of the line that passes by P(1, 2, 2) and that is parallel to the…

A: We have to solve above question of vector and 3D.

Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

A: The vector and parametric equation of a line passing through given point and parallel to given…

Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through (0, -7, 0)…

A: The given point and the plane is,

Q: a) Find the scalar parametric form of the equation of the line which is parallel to the line of…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

A: Given Data The equation of the plane is x+3y+z=9. The point at which line pass is: (1, 0, 3).…

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

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Q: Find the vector and parametric equations for the line through the point P(-4, -1, -3) and orthogonal…

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Q: Find the vector and parametric equations for the line through the point P(-3,0, – 3) and orthogonal…

A: Given data is:point P-3,0,-3 and plane -1x+1y-5z=1

Q: Find a vector equation for the line through the point P = (4, -2, -4) and parallel to the vector vv…

A: P= (4,-2,-4) is a point on the line.  And the line is parallel to v=(4,-1,4)  v is the velocity…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: u = < 0,2,2>  w = < 2,-2,0>  U× W is perpendicular to both u and w

Q: Find parametric equations for the line whose vector equation is (a) (x, y) = (3, –5) + t(1, –2) X =…

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Q: 5. Given the points P= (2,-4,-1) and Q= (5,-4,2) in space. A) Find the parametric equations of the…

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Q: Given a the vector equation r(t) (4 + 4t)i + (1 + 1t)j + (1 + 4t)k, rewrite this in terms of the…

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Q: Find the vector equation that represents the curve of intersection of the cylinder a? + y = 25 and…

A: Given equation of cylinder is, x2+y2=25

Q: 1. Assume that the line l1 passes through point A(1, –1,2) and is parallel to both planes P1 : x +…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

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Q: a) Find the scalar parametric form of the equation of the line which is parallel to the line of…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

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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 a.…

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Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane 3x + 2y + z = -4 and…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.