4. Write y as the sum of two orthogonal vectors, y, in L and y₁ in L Let y = YL = 1 and u = 2 7 Let I be the line spanned by u. YL+ = ⠀

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

A:

Q: 1. Let v = PQ where P = (3,4,0) and Q = (2, 3, 1) Find a vector u that is parallel to V but with a…

A:

Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

A:

Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

A:

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

A:

Q: Find any two non collinear vectors on the plane x-y-3z +6=0

A:

Q: Let l be a straight line that passes through the origin and is parallel to the vectors…

A:

Q: Find a vector orthogonal to the line x+y=1

A:

Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: 27. Determine the area of the parallelogram formed by the vectors u=[3,-2,5] and v=[-1,4,2].

A: Step 1:

Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

Q: Let V1 = 2 V2 = 0 2 V3 = 2 V4 = 3 Decide the dependence or independence of the vectors {V₁, V2, V₁}…

A:

Q: Let j TE 2 --- = 1 and u = = Write y as the sum of two orthogonal vectors, #₁ in Span{u} and 2…

A:

Q: Determine by inspection the linearly independent vectors !! O a. O b. O C. с. -8 12 4 -2 2 5112]…

A: To determine by inspection the linearly independent vectors.a -812-4, 2-3-1, 000b 51, 28c 4-26, 6-39…

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

A:

Q: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two vector.…

Q: Suppose the straight lines L₁ and L2 have respective vector equations 5 4 r1 = -3 + t 3 where s and…

A:

Q: P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane…

A:

Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

A: