. Given two vectors = w a = a2 show that

Q: Find the length of the vectors (a) 2i⃗ +3j⃗ −k⃗

A:

Q: If ū and i are two vectors, prove the identity ld + 레? + |d - 비? = 2| + 2|미2

A: This question is based on vector multiplication.

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: 1. Find the angle between the following two vectors. and

A: The given vectors,  8,-5 and -9,-7

Q: Suppose that i and v are vectors in R". If ū · ū = 4 and ||v|| = 9, then || 18

A:

Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

A:

Q: If v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

Q: For what values of b are the given vectors o , (smallest value)

A: Let m→=-12, b,3 and n→=b, b2,b  If m→ and n→ are orthogonal.

Q: Draw the following vectors in standard position in R2;.

A:

Q: Find the components of the vectors u, v, u + v, and u - v, where u and v are as shown in Figure.

A: Given:

Q: Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b five times as…

A:

Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

Q: If two vectors ? = 4? + 6? − 8? and ? = 6? − 8? + 4? are added together describe the characteristics…

A: If two vectors ? = 4i+ 6j- 8k and ? = 6? − 8? + 4? ar

Q: Find the angles between given vectors. (a) ā = 3i + 4j and b= 5i – 4j (b) a = 3i +4j - 5k and 5= 6i…

A:

Q: If v . w = 0, then the two vectors v and w are____

A: If v . w = 0, then the two vectors v and w are____

Q: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

Q: given the vectors u = (2,4) y = (- 1,3) and w = (2, -3) Determine the values ​​of α and β such that…

A: Given vectors are  U = (2,4) so we can write it as=  2i + 4j ( i is the unit vector in x direction…

Q: If v*w=0, then the two vectors v and w are................ .

A: The question is taken from the vector in which we have to prove the given vector identity and given…

Q: Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find:

A: (a) The angle between the two vectors u and v is computed by the following formula. cosθ=u·v|u||v|…

Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

A:

Q: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

A:

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 15i – 6j, V = 4i +…

A: Given, Vector U = 15i -6j        U = 152 +(-6)2 = 225+36 = 261 = 16.2 Vector V = 4i +13j         V =…

Q: Under what conditions are the following true for vectors u and v in R2 or R3? (a) llu +vll = llull +…

A:

Q: One of the following vectors lies in span{ 2+x + æ2, 3+-2a2} (A) 5 + 3x + 4x2 (B) 5 + 3x + 5æ? (C) 5…

A:

Q: In the given diagram, which is the equivalent of vector

A: sum of vectors of closed triangle is 0 if we choose one direction -- Here if choose anticlockwise…

Q: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: 42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

A:

Q: 1. To the nearest tenth, find the angle between the two vectors below. v = 3i – 2j w = 2i + 2j

A:

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

A:

Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

Q: 6. Given the following vectors, Draw: a) a-b b) 2c + a c) - (c-b) a X b of

A:

Q: Given the vectors à = and b =

A:

Q: Which of the following vectors represents - 2u + v?

A: Given,

Q: ind the value of a so that vectors U = ai + 9j and V = 3i + 3j are

A:

Q: If v = a1i + b1.j and w = a2i + b2 j are vectors, the product v . w, called the________ , is defined…

A: If v=a1i^+b1j^ and w=a2i^+b2j^ are vectors, the product v.w, called the __________, is defined as…

Q: Given the following vectors: ü =, i = Find u x v.

A:

Q: If u and v are orthogonal, what is the magnitude of u × v?

A: We define the cross product of any two vectors as :                            |u×v|=|u||v|sinθ…

Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: Suppose that u and V are vectors of lengths 2 and 3, respectively. If the angle between u and V is…

A: Dot product of two vectors u and v is given by

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 16i- 8j V = 3i+11j…

A:

Q: If north is the direction of the positive y-axis and east is the direction of the positive x-axis,…

A: we have to solve given problem:

Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

A:

Q: Given the following vectors: di = 3î – 2j, d, = -5î + 2j – k What is (di + dz) · (dị × (4dz))?

A: d1 =3i-2j+0k d2 =-5i+2j-k

Q: 4 3 Which weights should be used for b = a, vị + a2 V2 to obtain the vector b = ? 2 a1 = Ex: 42 az =

A: Solve the following

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree: u = 13î – 8î and 3 = 2î…

A:

Q: Given the three vectors A, B, and D, show that A (B +D) = (A · B) + (A · D).

A:

Q: One of the following vectors lies in span{ 2+ x +x², 3+x – 2x? } (A) 3 + 2x + 4x² (B) 3 + 2x + 5x?…

A: We have to find

Q: One of the following vectors lies in span{ 2+ x + x2, 3+x- 2x2} (A) 2+ 2x + 7x? (B) 2 + 2x + 5x? (C)…

A: The linear span of the given vectors is of the form a(2+x+x2)+b(3+x-2x2)

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

A:

Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.

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.