Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i – j + 2k) (b)6(2i – j – 2k) (c) (21- j- 2k) (d) 3(2i – j – 2k) 20

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y2 = 50 and y? + 22 =…

A: Find a vector tangent to the curve of intersection of the two cylinderx2+y2=50 and y2+z2=50 at the…

Q: 10) Find a unit vector in the direction that f (x, y, z)= 2x² +6xy² – xz' increases most rapidly at…

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

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

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Q: Find the directional derivative of f(x,y,z)=xeY+ye² at (0,0,0) in the direction of the vector…

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Q: Find the equation of the plane in xyz-space through the point P=(2,5,5) and perpendicular to the…

A: Given: The point on the plane is P= (2, 5, 5). The plane is perpendicular to the vector n= (1, -4,…

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…

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Q: The divergence of the vector G = 2i+ sin y j+ 3k is :- -8y + x3 -8y siny + cosy O Option 3 O Option…

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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 a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

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: The divergence of the vector G=i+siny j + 3k is :- -8y x3 + siny -8y x3 + cosy Option 1 Option 3…

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Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

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Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

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

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Q: Suppose the pathogen is currently at location (1, 1) in antigenic space. Using a vector projection,…

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Q: Find a unit vector tangent to the curve of 25 intersection of – x? – 2y3 = z - 3 and 4y – 3z? =- x+…

A: This is a problem of vector calculus.

Q: It is known that the acceleration vector for a particle is given by A(t) = 4j + 2tk. Determine the…

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

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Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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Q: Find a unit vector in the direction in which f (x, y, z) = 3x³z² + 3y°z + 24z – 4 increases most…

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Q: Find the directional derivative of in the direction of the vector (1,3) at the point (-1,2)

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Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* –…

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

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Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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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: Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25…

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Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: The electrical potential (voltage) in a certain region of space is given by the function V(x, y, z)…

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

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Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by < t^2+1, ln(2t+3) > for all t>=0

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

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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 a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

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

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Q: A vector with magnitude 4 points in a direction 265 degrees counterclockwise from the positive x…

A: Given  Magnitude of 4 points at an angle of 265° In counter clockwise direction  from positive x-…

Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

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 the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the…

A: topic - equation of a plane

Q: Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

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Q: a) Determine the gradient for the vector A = 4x'yz+ x²y²z² at point (2,-2,3) travelling %3D along in…

A: Given: A=4x2yz+x2y2z2 at point (2,-2,3)

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

A: