Q.2B) Evaluation of JA- 2B| through define length of the vector |A| equal to O and length of vector |B equal to ), Where angle between two vectors equal to e = (). %3D

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: Let u and v be two non-zero vectors in R". Which of the following options can we conclude are equal…

A:

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

A:

Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: 1) In the triangle that determined by the points P.Q and R, find a unite vector perpendicular to…

A:

Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

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: . For what values of c are the vectors [−8, c, 4] and [c, c^2, c] orthogonal?

A:

Q: Q1/ complete the fllowing sentences with suitable answer in the blanks: 1. For any two vectors X, Y…

A: Question (1) - X = x1x2Y = x1x2These two vectors will be equal only when x1=x2 and y1=y2.

Q: Use the accompanying figure to write each vector listed in Exer- cises 7 and 8 as a linear…

A: Given - Use the accompanying figure to write each vector listed in Exercise 8 as a linear…

Q: 4. Find a unit vector that points in the same direction as v = (1,3,9).

A:

Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

A:

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: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

A:

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: .b,č are three vectors such that a + b+ e = 0, lal = 5.6 = 3. = 8 then ä.b+ ans. -49 48 1/6

A:

Q: 10. Find a unit vector in the same direction as PQ if P = (5, 4) and Q (3, 7). %3D

A: The solution is given as

Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: Two vectors of magnitudes B= 5 and C = 3 are lying on the xy plane as shown in the figure. What is…

A:

Q: 3. The dot product of two orthogonal vectors is: A.undefined. B. Zero, C. Infinity.

A:

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: the angle made by vector A = 2 ax- ay +2 az and X-axis

A:

Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

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

A:

Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

A:

Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

A:

Q: 2 Let u = = 1 (i) Find the angle between u and v. (ii) Find a vector w of length 2 in the direction…

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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: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

A:

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: 3 Compute the length of the vector v =

A:

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

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

A:

Q: 7. Write the vector w in terms of u and v, given that the terminal point of w bisects the line…

A: This question is related to vectors, we will solve it using given information.

Q: Find the equation for the plane through the point Po= (9,2.5) and normal to the vector n= 31 + 10j +…

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Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

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

A:

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector CX - Czy. shect…

A:

Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

A:

Q: - ()--)- 1 Let a = 2 and b = be two vectors. What is Jal2|b|2 - |a · bl2 ?

A: Here,  Given that  two vectors  . So, we find the value of  |a|^2.|b|^ - |a.b|^2

Q: 1. Find the equation of the vector from SCS points P;(5, 45°, 30°) to P2(7,120°, 150°). Express your…

A: Given - P1(5,45°,30°) , P2(7,120°,150°) To find - The equation of the vector from P1  to P2 and…

Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

A:

Q: Q1. A- Find the cross product (uxv) of vector (u = i – 2j + 5k) and vector ( v=). Are the two…

A: Topic = Vector If the cross product of two vectors is zero it means both are parallel to each other.

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

A:

Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.