6. Find a vector which is normal to the currive: 3= 11 at (1,2). x³ + xy + y²

Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: Find a vector v parallel to the intersection of the planes - (x + y + 3z) = 4 and 3y - 3x - z = 7.…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: Find Düg(1, −1) where g(x, y) = e−(x²+y²) and u is the unit vector parallel to .

A: To find  is the unit vector parallel to .

Q: Find all points on the curve r(t) = ti + t²j+t³k where its tangent line is parallel to the vector…

A:

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: The vector value of the tension (T) in rope AB equals 8 m 12 m 2 m 4 m C G 11 m 2 m B 6 m 2 m Select…

A: To determine the correct vector value of the tension (T) in rope AB, we need to compute the vector…

Q: Let A(x,y,,z) and B(x,,y2; z,) be two known 3D points. The point M on the line AB divides the vector…

A: The vectors AB, AM and MB are collinear vectors. Therefore, consider the formula for the collinear…

Q: (3.) The distance of two vectors x and y, dist(x, y) =|| x-y ||= /(x – y, x – y). (a) Find dist(x,…

A:

Q: Find a unit vector with positive first coordinate that is orthogonal to the plane through the points…

A: Given that the points P-2,-3,-1 Q3,2,4andR3,2,7  .

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: Where does the line with the vector equation [x,y,z] = [6, 7, -8] + t[-2, 4, 1] intersect the…

A:

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

A: