Find a vector tangent to the curve of intersection of the two cyclinders a+ y? = 98 and y + 2 = 98 at the point (-7, -7,7). (2² + y° = 98 ve y² + z = 98 silindirlerinin kesigimine (–7, –7,7) noktasında teģet olan vektoru bulunuz.) Lotfen birini seçin: O 196i+ 98j+ 196k O-98i+ 196j+ 196k O 196i+ 196j+ 98k O-196+ 196) 196k O 147i+ 196j+ 196k

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

A: Explanation of the answer is as follows

Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

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

A:

Q: Let S be the square with vertices (0, 0),(1, 0),(0, 1) and (1, 1) and let P be the point (2, 0). Is…

A:

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 parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

A: The vector parametrization is:                                       r(t) = r0 + tv = x0,y0,z0 +…

Q: Find a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2…

A:

Q: Find a vector parametrization of the curve x = -3z² in the xz-plane. t as the parameter in your…

A:

Q: Find a vector function that represents the curve of intersection between the paraboloid 2 z = 4x² +…

A:

Q: Find a unit vector n that is normal to the surface 2z^2−x^4−y^4=1 at P=(1,2,3) that points in the…

A: We have

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

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 a vector tangent to the curve of intersection of the two cyclinders a? + y? = 8 and y? + 22 = 8…

A: Let fx,y,z=x2+y2 and gx,y,z=y2+z2 The gradient of the functions give the perpendiculars to the…

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 an equation of the plane. The plane through the point (8, 7, 1) and with normal vector 7i + j -…

A: The equation of the plane is given as:

Q: Find an equation of the plane through the point (4, 5, 1) and with normal vector 6i + j - k. Show…

A: The plane passing through a point A(a) with the normal vector n is given by: r·n=a·n where,…

Q: The plane with normal vector - 7) containing the point (4,-1,1) has equation Ar + By + Cz = D. If A…

A:

Q: Find the normal vector to the tangent plane of z = 4e"² - 6y at the point (12, 24, 4). x component y…

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: Give an equation of the plane with a normal vector n = ⟨1, 1, 1⟩ that passes through the point (1,…

A: we know that equation of plane with a normal vector x0,y0,z0 and passes through point x1,y1,z1 is…

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

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

A:

Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1)…

A: To find the vector parameterization for the line that passes through the point (1, 1, 1) and…

Q: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

A:

Q: Find a unit normal vector to the surface 6x2 + 2y2 + z2 = 225 at the point P : (5, 5, 5), and…

A:

Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

A:

Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=<0,-2,1>Hence, Vector…

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 the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

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 the Directional Derivabive of Pary,2)= x-yz'+ at the point CI, -2, 0) in the direcbion of…

A: A scalar function is a rule to associate a number to a particular point in space. The directional…

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 an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

A: The vector equation of a plane is given by the expression . Here, and are the vectors that lie on…

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: 2. If A is the position vector of the point p-(x,y,z) and A=A. And ifr is the radius of the point in…

A: We apply the cross product to find the given function and simplification needed.

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

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 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: (8) Find a vector parameterization of the line r(t) which passes through the point P = (1,2, –8)…

A:

Q: Find a vector function that represents the curve of intersection of the paraboloid z = x^2 + y^2 and…

A: Intersection of paraboloid and cylinder can be obtained by representing y in the form x and z in the…

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

A:

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 +y? = 200 and y? + z2 =…

A:

Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Find a vector tangent to the curve of intersection of the two cyclinders a2 + y? = 8 and y² + 22 = 8…

A:

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

A:

Q: 2

A:

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.