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 length given by ||u|| = 6v/3

Q: Let u = (-5,-2, 4), v = (3,6,-5) and w (-7,1,-8). (a) Calculate (u x v). w and hence find the volume…

A:

Q: Let u and v be vectors in Rn. Show that 1 1 |||u + v||² − − ||u − v||² . - 4 u. V =

A: Given: u and v are vectors in Rn We are required to prove: u.v=14u+v2-14u-v2

Q: a) Let i = xî + yj + zk, r = |7| and å is a constant vector. Find the value of %3D dxr div

A: We will find out the required value.

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: 13. Consider the position vector i = (1,0, 0) in R³. Describe the set of position vectors v in R³…

A: Given, i=1,0,0∈ℝ3

Q: 11. Given vector u = (2, a, 3), vector v = (1, -3, b) and u x v = (13, -5, -7). Find a and b.

A:

Q: Find x∈R such that vectors a = and ?=. are equivalent

A:

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

A:

Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

A:

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: Find the length of the vector v = (9, 3, 9). ||v|

A:

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

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: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

A:

Q: (a) Find the best approximation to ✅ by a vector of W. (b) Write as the sum of a vector in W and a…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Let W be the set of all vectors of the form 111 ū= -3s- 2t 2s+t -s-2t Find vectors u and 7 in R³…

A:

Q: L is a line in 2-space or 3-space that passes through the points A a then the distance from a point…

A:

Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

A: