Find a vector equation for the line through the point (-4, 8, 2) perpendicular to the plane –7x – 7y + 7z = 16. 7(1) = with -co < t < ∞

Q: Evaluate the volume between the surface z = 3 + 2x + xy, and the rectangle in the xy plane given by…

A:

Q: The unit vector from A(4, 2) to the point B(-2, 10) is:

A:

Q: A = (2, -4) and B = (-3,3). Determine the distance between points A and B and find their polar…

A: Two points given in the xy plane  A = (2, -4) and B = (-3,3)   Find: Distance between the A and B…

Q: Consider the vectors A = (-5.4, 8.8) and B = (8.7, -9.4), such that A - B + 3.8C = 0   What is the x…

A: Let the coordinates for point C be (x, y).For the given coordinates of A and B, vector…

Q: Consider a rectangular surface of length L and width W in the xy plane with its center at the…

A:

Q: Solve the quadratic equation 5.00t2 − 4.00t − 6.00 = 0 using the quadratic formula, finding both…

A: General form of quadratic equation is,

Q: If the Cartesian coordinates of a point are given by (-1, y) and its polar coordinates (r, 120°).…

A: given that    Cartesian coordinate =( -1 , y )  put  X = -1    Y = y polar coordinate =( r, 120°)…

Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: Find the arc length of the space curve given by the vector function r (t) t3 i + t2 j + (2t + 1) k…

A:

Q: Given two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }

A: To solve the given question, we will write down the given two vectors in vector form and then we…

Q: Show that for orthogonal coordinate systems gij= 0 for i not equal to j

A:

Q: Suppose thatP = (x, y) has polar coordinates(r, θ ). Find the polarcoordinates for the points:  (−x,…

A: Given: The point P is (x,y). The polar coordinates are (r,θ). The coordinates of the point are…

Q: Calculate the angle between vectors A=î+3ĵ+2k and B=î+27+3R

A:

Q: Find the angle between the two vectors Ả = 2 î + 3ĵ + k B = -4 î + 2ĵ – k and

A: Given  A=2i+3j+k B=-4i+2j-k

Q: Show that the force vector B = 2î – 4ĵ + k is orthogonal to the force vector ở = 3î + 43 + 10k. [2]

A: There are Two vectors -

Q: Consider the vectors A = (-8.1,5.4) and B = (10.7,-9.1), such that A - B +2.7C = 0. %3D

A:

Q: If A = 4i − 3k and B = −2i + 2j − k, find the scalar projection of A on B, the scalar projection of…

A: The given vectors are, A=4i-3kB=-2i+2j-k

Q: Find the vector v in the xy-plane with magnitude 5 if the angle between v and i is 150°.

A: Given data: Magnitude of the vector, v=5 Angle, θ=150°

Q: Find the cosine of the angle between vector R= 4.3î + 2.1ĵ+7.3k and the positive direction of…

A:

Q: Find the divergence and rotation of the following vector A=i(x^2+y^2)+j(y^2+zx)+k(z^2+xy)

A:

Q: What is the angle e between vectors à and B if A = 3 i +4 ĵ and B = 8 î – 6 j?

A:

Q: Show that the points with position vectors 3i-5j, 4į+j, 6¿+13j are collinear. If the point whose…

A:

Q: Suppose the vectors i, j, pand q are all unit vectors and the angle 0 = 340°. Find the cartesian…

A:

Q: Let vector A  point from the origin into the second quadrant of the xy plane and vector B point from…

A: When subtracting vectors, the rule is to graph the first two from the origin and then connect them…

Q: Let C be the plane curve given parametrically by the equations : x(t) = t² - t and y(t) = t² + 2t -…

A:

Q: Find the distance from the origin to the plane 3x − 2y − 6z = 7

A: The equation of the plane is, Now, compare the above plane with the general form of the plane (ax +…

Q: Three points, A, B, and C, exist on an XY-plane. The positions of points A and B are (3,1) and…

A:

Q: Find the measures of the angles between the diagonals of the rectangle whose vertices are A = (5,…

A: Vertices of rectangle: A(5,6), B(8,12), C(-40,36), D(-43,30)  When we'll plot these vertices on…

Q: Suppose the vectors i, j,pand q are all unit vectors and the angle 0 = 131°. Find the cartesian…

A: Required : The force in p and q coordinates.

Q: nates of point N. 2) Write the vector KM in terms o

A:

Q: Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there…

A: Let’s consider the following sets of vectors,

Q: : Express the vector 2i + 3j – k in the primed triad i'j'k' in which the x'y' axes are ated about…

A:

Q: Which of the following is the conserved quantity if the system having Lagrangian L= = m(x² + y²) – ²…

A:

Q: Let be two vectors, such that a=(3+2j-2k) cm and b=(2î+2j+k) cm, calculate: 1) The angle between the…

A:

Q: Find the scalar and vector projections of a and b if a = 3i − 3j + k and b = 2i + 4j

A:

Q: Solve the quadratic equation  3.00t2 − 4.00t − 6.00 = 0  using the quadratic formula, finding both…

A:

Q: Consider two vectors A= 6.75 i+(-3.53 k) and B= (-4.1j)+1.08 k. Find the angle between these two…

A:

Q: Prove the property of the cross product u × v = 0 if and only if u and v are scalar multiples of…

A: The cross product property of vectors is given by:u×v=uvsinθ......(1)where,u and v are the magnitude…

Q: Find the direction cosines of the vectors whose direction Ratios are (3, 4, 5) and ( 1, 2, -3).…

A:

Q: Given ϕ=xy+yz+xzϕ=xy+yz+xz, find gradient ϕ at point (1, 2, 3).

A: