The surface of a hill is modeled by z = 100 3x – 4y2. When a group of hikers reach the point (2, - 2, 72) it begins to snow. They decide to descend the hill as rapidly as possible. Which of the following vectors points in the direction they should start their descent? O < 12, - 16 > < - - 12x, 16y > < – 12, 16 > < 12x, – 16y >

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

A:

Q: Add the vectors u (0, 3) and i = (- 2, – 1) graphically. Your graph should include u, v and the…

A:

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

A: vector equation can be find in the following way:-

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

A:

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A:

Q: Find an equation of the plane that passes through the point (0, 0, 0) and is perpendicular to the…

A: The direction ratio of n = −3i + 2k is (-3,0,2) Given that that plane is perpendicular to n = −3i +…

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

A:

Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find a vector that has the same direction as 8i-j+4K but has a length of 6

A:

Q: Find two vectors v1 and v2 whose sum is (2, –5), where vj is parallel to (5, 2) while v2 is…

A:

Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

A:

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

A:

Q: 10

A:

Q: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (2,6, –1) and…

A: To find equation of line passing through the point 2,6,−1 and perpendicular to both vectors −4,3,−5…

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: The intersection of the two planes given by the vector equations ()- -2 =0 r. and -4 = 3 r. is

A:

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

A:

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

A:

Q: Find the vector in the same direction as &lt;1, 1, 0&gt; whose component in the direction of &lt;2,…

A: Let  us suppose that

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: Find the vector that has the same direction as (6, 2, -3) but has length 2.

A:

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: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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: Give the parametric and symmetric equations of the line that passes through the point (4, –3,5) and…

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: Find the general form equation of the plane through the origin and perpendicular to the vector (4,…

A:

Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: Find the vector that has the same direction as (2, 6, -9) but has length 4.

A:

Q: Find an equation of the plane that is parallel to the vectors and , passing through the point (3,…

A: Use given parallel vectors &lt;1,-3,1&gt; , &lt;4,2,0&gt; and passing through the point (3,0,-2)…

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A:

Q: Find two vectors and 02 whose sum is (2, –4), where is parallel to (2, -4) while vz is perpendicular…

A:

Q: Find the equation of the plane in xyz space through the point P= (3,3,4)and perpendicular to the…

A: We need to find equation of plane.

Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

A:

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

A:

Q: Find an equation of the line that goes through A(0, 1, 4) and is orthogonal to the Y-axis and vector…

A:

Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Write the vector A = 2z1-xi + yk in cylindrical coordinates.

A: *concept:- cylindrical co-ordinate = (x, y, z).

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A:

Q: Is the line passing through the point (3/2, 1) and slope −2 a hyperplane ? If yes, identify this…

A: Any line in 2D is a hyperplane.  ax+by=c, is a hyperplane (a,b) is called the normal vector  c is…

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

A: Questions from vector calculus.

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A:

Q: The equation of plane through (3,-1,7) and perpendicular to the vector (4,2,-5) is 4x + 2y5z-25 = 0.…

A:

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

A:

Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

Q: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.