(B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k dw (C): If w = tan x and x = 4t³ +t; Find ? dt

Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

A:

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 a unit vector parallel to the line y = 7x – 3. Use the scalar product to find the angle between…

A: The equation of given line is:.Suppose,.So,.So, the parametric equation of the line is:So, the line…

Q: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

A: WE know that equation of line through (x1,y1,z1) and parallel to vector ai+bj+ck is

Q: Determine the magnitude of the vector difference V' = V₂ - V₁ and the angle 0x which V' makes with…

A: We have to solve given Questions.

Q: Find a vector in component form that is perpendicular to the line 3x 4y = 6.

A: To find the vector in component form that is perpendicular to the given line.

Q: Use the vectors u = (7, 7), v = (-6, 4), and w = (5, -3) to find the indicated quantity. (u · 2v)w…

A:

Q: Calculate the cosine of the angle which the vector 2i+2j-k makes with the positive x-axis

A: Given: find the cosine of the angle which the vector 2i+2j-k makes with positive x axis

Q: Find the angle between the vectors r = (-1, 2) and s = (4, 2)

A:

Q: Determine the magnitude of the vector difference V' = V₂ - V₁ and the angle 0x which V' makes with…

A:

Q: y =-x (b) Use it to project the vector v =

A: Given

Q: Determine the magnitude of the vector difference V¹ = V₂ - V₁ and the angle 0x which V' makes with…

A: Here,

Q: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.