10. Given two vectors u =6,2] and v = [-2,1), determine the projection of u on v.C %3D %3D

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

A:

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: 10. Given two vectors u = [6,2] and v=[-2,1], determine the projection of u on v.

A: #10

Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

A:

Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

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: Suppose U and W are vectors in R" then ||U +W|| - ||U|| + || W|| if the angle between U&W is equal…

A:

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: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

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: Solution :

Q: 1 Compute the orthogonal projection of v = onto the line L through -6 and the origin. 2 projz (7) 2.

A:

Q: 11. If ā.b = 0, why can we not necessarily conclude that the given vectors are perpendicular? (In…

A:

Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

A:

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

A:

Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: 2. The cross product of two vectors u and v is. to u and to v. Thus if both vectors u and v lie in a…

A: Given two vectors u and v

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

A:

Q: 6 2 Show that it is vectors are lineas dependent line or independent.

A:

Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

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

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: 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: Suppose we know that u · v = u · w. Does it follow that v = w? If it does, give a proof that is…

A:

Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

A:

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

A:

Q: A set of 3 vectors in IR^4 spans IR^4. Is this true or false?

A: Given statement is, “A set of three vectors in R4 spans R4.”

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

A:

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) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

A:

Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

A:

Q: What is the value of each of the constants that are part of the linear combination between the…

A:

Q: given the vectors from R3 v, = (2 0 3), v2= ( -1 3 0), v3=(2 4 –1) %3D (-5 0 3) belongs to span{v,,…

A: Given vectors are v1→=2,0,3, v2→=-1,3,0, v3→=2,4,-1. To determine: u→=-5,0,3 belongs to span v1→,…

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

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

A:

Q: 8. If the vectors in the figure satisfy |u| = |v|= 1 and u + v + w = 0, what is w ? u W V

A:

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: We will use expansion of u-v to find the angle

Q: 17 jp 17 Jlgull>> حفظ الإجابت 3 درجات Two vectors ñ and m are said to be parallel if ñ m-0

A:

Q: A- If P1(1,3, –2) and P2(4,7,-2) are two points. 1- Compute the length of 2P,P2 2- Is the vector…

A:

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: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

Q: given vectors u=4i-j and v= 3i+3j compute the projection of v onto u?

A: Given, vector u and v

Q: Use the given pair of vectors u = (- 3, – 4) , v = ( – 4, – 4) to compute u + v = u - v = 2u – 3v

A: <a,b> + <c,d> = <a+c , b+d>

Q: Show that for any two vectors u and v: = |

A: