Use the geometric definition of the cross product and the properties of the cross product to make the following calculations. (a) ((i + j) × i) x 3=

Q: Verify that the two lines are parallel and find the distance between the lines. L1:   x = 2 − t,   y…

A:

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A:

Q: Use the above formula to find the distance from the point to the given line. (0, 2, 1); x = 3t, y =…

A:

Q: Determine the angle between the following two planes: 4x - 3y2z - 2 = 0 3x + 2y + 5z-5=0

A:

Q: Find the point at which the line intersects the given plane.

A:

Q: find the coordinate of point x such that the ratio of MX to XJ is 2:3

A: Let Position vector of point M and J be m→ and j→, respectively. Point X divides segment MJ into the…

Q: Verify that the lines are parallel, and find the distance between them L1: x = 2 - t, y= 3 + 4t, z =…

A:

Q: Find the angle between xy=3 and x²=9y

A: The given curves xy=3 y=3/x    ....(1) x²=9y   ....(2) Solve equation (1) and (2) x2=9×3xx=3y=x/3=1

Q: Q1/ Find the angle between the planes 3 x -6y - 2z = 15 and 2 x +y– 2z = 5

A: Explanation of the answer is as follows

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A:

Q: Calculate the cross product assuming that u x w = (-8, -1, -5) (5u + 3w) x w =

A: Solution

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A:

Q: Find the acute angle between the lines x + 2y = 7 and 5x – y = 2. %3D

A:

Q: Find the values of x and y in parallelogram PQRS. PT y, TR 3x+ 1, QT = 3y, TS = 5x + 11 and y =

A: The diagonals of a parallelogram bisect each other.  So, PT=TR or y=3x+1 And QT=TS or 3y=5x+11

Q: Parallelogram WXYZ and diagonal WY are shown in the diagram below Y Which of the following…

A: For the solution follow the next step.

Q: Find the distance between the lines: ri = +! r2 = + s

A: We have to find the distance between given 2 lines.

Q: Find the cross product (i+ e'j +e*k) ) × (2i + e'j – e-'k).

A:

Q: Find the angle between the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5.

A: Given equations of the planes3x-6y-2z=15 and2x+y-2z=5we have to find the angle betweenthem θ

Q: Find the angle between the line given by ⟨x, y, z⟩ = ⟨2t, 3t, t⟩ and the y-axis exactly.

A:

Q: Find the distance between the parallel lines.

A: To find the distance between two parallel lines are                                          d…

Q: Find the cross product a × b. a = (t, t2, t3),      b = (1, 6t, 8t^2)

A:

Q: Use the right-hand rule and the properties of the cross product to make the following calculations.…

A:

Q: Calculate the cross product assuming that u x w = (-3, 6, 6) (4u - 4w) × w = |

A:

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A:

Q: Find the cosine of the angle between the planes  x + y + z = 0 and x + 4y + 3z = 2.

A: The two planes be  a1x+b1y+c1z+d1=0a2x+b2y+c2z+d2=0 let the angle between the planes be α  Then cos…

Q: Find the angle between the planes 3x-6y – 2z = 15 and 2x +y – 2z = 5

A: Recall: Vector method, cos θ=n1·n2n1n2 We have, n1=3i-6j-2k, n2=2i+j-2k

Q: Find the cross product a x b. a = i + e'j + e-tk, b = 5i + e'j - e-tk

A: The cross product of a and b is:

Q: The cross product of A = 4i + 2j with B is zero. The dot product of A •B = 30. Find B.

A:

Q: Find x and y for the parallelogram. 4y° 4x° 14x X= y3D

A:

Q: Find the distance between the planes – 3x + 5y = 32 and – 3x + 5y = 27.

A: Simply use the formula for the distance between two planes.

Q: Calculate the cross product assuming that u x w = (-7, 1, -6) (2u + 4w) x w = = (

A: To calculate the cross product of 2u+4w×w, assuming that u×w=-7, 1, -6.

Q: Find the distance between the parallel planes – 2x + y + z = 0 and - 10x – 5y – 5z – 11 = 0. - NOTE:…

A:

Q: Determine the angle between the following two planes: [1T/2A] 4x - 3y2z - 2 = 0 3x + 2y + 5z - 5 = 0

A:

Q: Find the cross product á xb and verify that it is orthogonal to both á and b for á = i+ 33 – 2k and…

A: Given:-a→=i→+3j→-2k→b→=-i→+5k→To find: cross product a→×b→

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A:

Q: Find the angle between A-10, + 2a, and B--4a, + 0.5a, using both the dot product and the cross…

A:

Q: Find the distance between the plances 3x + y – 4z = 2 and 3x + y – 4z = 24

A: Given the two planes 3x+y-4z=2,3x+y-4z=24. The distance between two planes Ax+By+Cz=d1,Ax+By+Cz=d2…

Q: Find the angle of intersection of the following curve. xy = 6 and x'y = 12

A: As we know that the expression for angle of intersection of two curves is:…

Q: Calculate the cross product assuming that u X w = (-2, -3, -2) (2u + 4w) × w = {

A: Given u × w = -2, -3, -2

Q: Use the geometric definition of the cross product and the properties of the cross product to make…

A:

Q: Find x and y for the parallelogram. 4y 25x 75 64x X3D y%3D

A: Since parallel sides of a paralleogram are equal,  25x = 75 and 64x = 4y

Q: Find the distance between the plances 3x + y - 4z = 2 and 3x + y – 4z = 24

A:

Q: Find the cross product a × b.

A:

Q: Use the geometric definition of the cross product and the properties of the cross product to make…

A:

Q: Find the values of x and y in parallelogram PQRS. R PT = y, TR = 3x + 1, QT = 3y, TS = 4x + 13 P and…

A: We can find the value of X and Y using the properties of parallelogram as below

Q: Determine the angle between the following two planes: −x + 6y + 3z − 6 = 0 2x + 3z − 10 = 0

A:

Q: (b) Use the cross product to derive the distance formula between the point Q and the line l PQ × PŘ…

A:

Q: Find the angle between y=5x2-3 and 3xy-9x2-x

A: Given y=5x2-3 --- Eq 1 and 3xy=9x2-x      --- Eq 2We know that angle between y1=k1x+b1 and y2=k2x+b2…