Two planes have equations x + 3y – 2z = 4 and 2x + y + 3z = 5. The planes intersect in the straight line I. (i) Calculate the acute angle between the two planes. (ii) Find a vector equation for the line I.

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

A: A)x, y =3, -5 + t 1, -2x, y =3, -5 + t, -2tx, y =3+t, -5-2t Parametric equations of the line:x= 3 +…

Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…

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Q: Find the equation of a plane that is perpendicular to the vector – i+ 2j+ 2k and passing through the…

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Q: How would I solve this? Find an equation of the plane that passes through the given point and is…

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Q: Write the vector equation for the line of intersection between the planes π1:x−z=−5 and π2:x−y=−1.

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

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Q: 3. Determine the vector equation for the line with symmetric equations*=3+22=1

A: Given: Symmetric equation of line: x-34=y+25=z-13 To find: Vector equation of line.

Q: The surface of a hill is modeled by z = 100 3x – 4y2. When a group of hikers reach the point (2, -…

A: Given that, z=100-3x2-4y2And point is 2,-2,72

Q: Give the equation of the line in vector form, parametric form and symmetric form. The line through…

A: Given line is  The direction ratios of given line are proportional to <-3,9,-1>. Since the…

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 parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

Q: Find the equation of a plane that is perpendicular to the vector 3 i - 4j+ 5k and passing through…

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Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

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Q: Find the equation of a plane that is perpendicular to the vector i+ 2j+5 k and passing through the…

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Q: Determine the vector equation of the plane 5x – 2y + 3z + 24 = 0. Verify mathematically that your…

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Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

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

Q: Which of the following is a direction vector for the plane with Cartesian equation 3x -2y - 5z + 3 =…

A: To find a direction vector for the given plane. The general form of plane with cartesian equation…

Q: 2. Start with the vector =(2, 1) a) Rotate the vector 55° counterclockwise and sketch the resulting…

A: Given: The vector x→=2,1. To find: a) the resulting vector after rotating the vector x→ by 55o. b)…

Q: 2. Start with the vector -(2, 1) a) Rotate the vector 55° counterclockwise and sketch the resulting…

A: Topic = vector

Q: (A) Find the unique point P on the y-axis which is on both planes. (B) Find a unit vector u with…

A: (a) ... Unique point on the  y axis on the both planes  On the y axis means, x and z=o  Which means…

Q: Find both the vector equation and the parametric equations of the line through (-3,3,7) and (3, -…

A: Consider the points <-3,3,7> and <3,-1,0>. The vector equation and the parametric…

Q: A line has y-intercept 11 and z-intercept -13. Find a vector equation of the line.

A: The line has y-intercept 11 and z-intercept -13. So the line passes through points A(0,11,0) and…

Q: A pilot is heading his plane N 76°W at an airspeed of 950km/h, while wind is blowing in the…

A: Given: A pilot is heading his plane N 76 degree W at an airspeed of 950 km/hr, while wind is blowing…

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

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Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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

A: Given point is (0,4,0) and normal vector is -7i+5j.

Q: A plane traveling with a velocity measured in meters per second, is described by vector a = (-6,5) .…

A: Let's find.

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 passing through the point perpendicular to the given vector or line.…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  . the given direction…

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: х-2 у-4 Convert the symmetric equation of the line l: to the vector equation. 6. 7

A: Here we have to convert the symmetric equation of the line l:(x-2)/6=(y-4)/7 to the vector equation.

Q: Vector u has a magnitude of 28 and a direction of 60 degrees. Vector v in component form is (c,…

A: Firstly we will use the angle and the magnitude to get the linear standard form. Moreover, we will…

Q: If the vector equation of a line is 7=(3, -5)+t(-2, 3), t€ R. the parametric equations are Ox=3-2t,…

A: Topic:- application of geometry

Q: Find the parametric equations of the line containing the point (-2,1,2) and parallel to the vector…

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Q: Give a vector parametric equation for the line through the point (-1, –1) that is perpendicular to…

A: We have to write a parametric equation of the line  which is passing through the point (-1, -1)…

Q: b. A tennis ball is served horizontally from 2.4 m above the ground at 26m/s. The net is 11.5m away…

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

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Q: What is the equation of the vector in a Cartesian coordinate system that originates from the origin…

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Q: a) Find the symmetric equations of a line through the point po(2,-3,5) and perpendicular to the…

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Q: Give a vector parametric equation for the line through the point (-2, –2) that is perpendicular to…

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Q: A line has parametric equations x = 2 +3t, y = 1 + 2t, z = -6 - t, fort that belongsto the family of…

A: given parametric equation of line  is x=2+3ty=1+2tz=-6-t

Q: a) Does the point P(2, −1, −3) lie on the plane given by Π : 2x − y − 3z − 4 = 0? Justify your…

A: Here in this question we have to find out the equation of a line passing through point (2, -1, -3)…

Q: Find the equation of a plane that is perpendicular to the vector 4i+4j−3k and passing through the…

A: On solving this we will get

Q: Consider the line with vector equation r(t) = (2t, t+1, t) and the point (1, –3, 2). a. Find the…

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Q: 10. Find the vector equation of a line whose symmetric equations are Xー1 y+3 z - 1 %3D %3D 3 -4…

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.