1. The vector in the opposite direction to u = (-2, 2) and of half its length is 2. The vector of length 3 and in the same direction as v = (-3, –5, 4) is

Q: Find a unit vector that is orthogonal to both u = (2, – 10, 8) and v = (4, 6, – 8).

A:

Q: For this problem, consider the points P = (-2,8,9) and Q = (0, 4, 5). (a) Express the vector PQ as…

A: As per our guidelines , we can only solve first three sub-parts. Please resubmit other questions as…

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

Q: Suppose that u and v are vectors in R' both of length 2/2 and that the length of u – v is also2 /2.…

A: The solution is give as

Q: according to what you learned from the vector addition experiment, if we have vectors à = 2.4x – 3ŷ…

A: Given that,a→=2.4x⏞-3y⏞b→=4x⏞+5.5y⏞x⏞ and y⏞ are unit vectors representing positive x and y…

Q: Suppose that u, v are vectors in R3 , u · v = 1, ||v|| = 1, the angle between u and v is π/3, and u…

A: The detailed solution is as follows below:

Q: 8 Find a vector of length: (2) (+) 3 a 10 units which is perpendicular to (a -4 b 3/2 units which is…

A:

Q: Suppose u = (-6,4, –5). Mark each vector below with a "T" if it is perpendicular to u, and an "F" if…

A: The given vectors u=-6, 4,-51. 2, 3, 02. 5,-2, 23. 9,-24,-304. -5,-4,-1

Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: 2. The two unit vectors parallel to the line 3x + 4y = 1 are and 3. The two unit vectors…

A: 2) The line is 3x+4y=1. Rewrite the equation of the line in the slope intercept form as,…

Q: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

A:

Q: 2; Find a vector of magnitude 3 in the direction v = (0, 3, –4)

A: The given direction is 0,3,-4.

Q: Is it true or false that the vector u = (3, 3, –3) is a direction vector to the line x + y+ 2z = 6 l…

A: I have written equation of line in parametric form and then checked the direction ratio

Q: Find a vector of length 5 in the direction of (2, 1). O A (V2,1) В. (2/5, V5) OC. (10, 5) O D. (2,…

A: see 2nd step.

Q: Find the vector equation of the line that passes through point M(1, 1, 2), intersects the following…

A: Question is solved.

Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

A:

Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

A:

Q: the component of vector a are ax=2.0 units and ay=3.0units while that of another vector b are Bx=…

A: Given components of two vectors: Components of a are: ax=2.0 units and ay=3.0 units, Components of b…

Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

A:

Q: 6. For the vectors ü = (4, 3) and i= (-2, 3), caleulate the following quantities. (a) la+ 레 (b) la+…

A:

Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

A:

Q: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: through the point (−2,4) and is perpendicular to the line  x=[31]+t[4−5] is

A:

Q: Find a vector perpendicular to d = [5,–4,6] and h = [-1,3,9].

A:

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Which vector below is NOT orthogonal to i = -2î – 8ŷ + 7k ? -- 1 2 8. O 0 î + 0ĵ + 0k 3. 1 O 4 î - )…

A: Given problem:-

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: (2) For the vectors ä = (-1,3, 4) and 5= (-2,2, 0) calculate the following: (a) ãoË (b) ä x b (c) A…

A:

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

A:

Q: 1. The vector in the opposite direction to u = (-1,0) and of half its length is 2. The vector of…

A: 1.The vector is u=&lt;-1,0&gt;2.The vector is v=&lt;-4,5,-3&gt;

Q: Q1) If a vector gets multiplied by a positive number, its direction * .will be reversed

A: Given statement : If the vector gets multiplied by a positive number, it's direction will be…

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

A:

Q: Find a unit vector in the direction of u = (5, 3, 2).

A: Given vector is u=(5,3,2) Find a unit vector

Q: Suppose that u, v are vectors in R³, u · v = 1, || = 1, the angle between u and v is T/3, and u is…

A: According to the problem, we have

Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

A:

Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=&lt;2,-2,1&gt;.

Q: In what direction should one move from the point (2, 3) to increase 4x?y most rapidly? Present your…

A: The solution is given below

Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

Q: b) Find the angle (0) between vectors between s [1, –5, 4] and t = [3,3, 3]. %3D

A:

Q: 13. Describe the vector that translates LMN to L'M'N’. 6. L' L 2 N' M -6 -4 -2 4 6 N2 M -4 -6 4,

A: Translation vector

Q: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

A:

Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: Find the given vector. Vector v of length 4 in the direction of = (-4, -4)

A:

Q: Prove that in R², the vectors {v1, v2, V3} are always dependent. What about if we have two vectors…

A: