4. Let Ā = -(1+ 2 )î + 7j – 5k , B = xiî + (6 +0)j – 2k and ĉ = (8 + 2 )î – 2k , find the following: a. If 2 Ā– B = 4 C , find the value of x. b. Show whether the vectors à and Č are perpendicular.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

Q: The following diagram shows the parallelogram ABCD. B A D Let AB =p and AC=q. Find each of the…

A:

Q: Q3/B/ For what value of 2, the vectors 2i – j+ 2k and 3i + 21j are perpendicular?

A:

Q: If r1,r2 and r3, are three parallel vectors of the same magnitude, Prove that r1+r2+r3 is equally…

A: GIVEN: r1 , r2 , r3 are three parallel vectors

Q: #1. The area of the parallelogram spanned by the vectors v = (A) – 22 (B) 22 (C) 23 (D) 8 (E) 2 (5,…

A:

Q: The unit vector which is perpendicular to both r138ax+3ay-2az, * r2=2ax+7ay-6az is equal to a)…

A: As per our guidelines, we are allowed to answer only question. Since, you have posted multiple…

Q: If u = 5i - j+ k, v =j - 5k, w = -15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)…

A:

Q: Q3/B/ For what value of 2, the vectors 2i - j+ 2k and 3i + 22j are perpendicular?

A: We can use the concept of perpendicular vector their dot product is zero.

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

A:

Q: B- For what values of a1 are the vectors [a1,4,3] and [3,-2,12] are 1) Orthogonal? 2) Parallel? 3)…

A: Angle between two vector

Q: 4. Let Ā = -(1+ m)î + 7j – 5k ,B = xî + (6 + n)j – 2k and C = (8+ m)î – 2k , find the following:…

A: Given data is : A→=-1+mi+7j-5kB→=xi+6+nj-2kC→=8+mi-2k

Q: (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three…

A:

Q: Find the positive value for which the vector r(t) (2t, 9t?, 10t2 – 2) is perpendicular to r'(t). -

A:

Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: Given vectors u = 2xi + 9j and v = xi - 4j, find x so that u and v are orthogonal.

A:

Q: For what values of c are the vectors t + 3 and 2t + c2 + 2 in P1 linearly independent?

A: t+3  &  2t+c2+2 Now since these vectors must be linearly independent, therefore…

Q: If a = 2i -j+2k and b =i+2j-2k, find two vectors c and d satisfying all the following conditions:…

A:

Q: given u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  determine a,b so that v are parallel vectors

A: Given that, u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  We have to determine a,b so that u and v are…

Q: Given v = 2i + 4j, w = -3i + 6j, find projw v. Then decompose v into two vectors, v1 and v2, where…

A: *The given vector v is, v=2i+4j *The vector w is, w=-3i+6j The projection of the vector on the other…

Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: Let a and y 6 Find the vectors v = 5x, u = x + ÿ, and w 5a + %3D || ||

A:

Q: HW/ O Find A.B, ĀXB For As i+ 3j+2k , B = K O let À - i+2j-K , B=-i+j+ K , E=i+k> Dz i+2j=K_ which…

A:

Q: Given v = 2i + j, w = 6i + 3j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A:

Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: Given v = - 3i + 5j and w = i+j, a. Find projwv. b. Decompose v into two vectors V1 and V2, where V1…

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: Given v = - 7i + 5j and w= -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

A:

Q: If a = 2i – j+2k and b =i+2j – 2k, find two vectors e and d satisfying all the following conditions:…

A: Let the required two vectors c and d be c=x1i+y1j+z1k and d=x2i+y2j+z2k. Now as per the given data,…

Q: For the given vectors a and b, find the cross product a x b. a = i +j+ k, b = 5i - 2k

A:

Q: 41. For what values of t are the following pairs of vectors parallel? (a) 27 + (r² + 71 + 1)j +ik,…

A:

Q: 3 Consider the vectors a= =(2³₁) and b =(p+¹). 2p 8 Find the possible values of p for which a and b…

A: we have to find p.

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+fk where a = 3, b = -3, c =…

A:

Q: Given v = i + 2j, w = 3i + 6j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: v=i+2j, w=3i+6j Now, v·w=i+2j·3i+6j=13+26=15 & w=32+62=45 Therefore,…

Q: 2) Let u=5i-j+k, v=j-5k and w=-15i +3j-3k. Which vectors, if any, are: a. Perpendicular? b.…

A: To find out the vectors which are parallel and perpendicular.

Q: 1 -E---Fl 2 V2 = 0 , and v3 = -5 span R³? Why or why not? 3 Do the vectors V₁ = -31

A:

Q: Q3: Find the angle between two vectors in space A = 41 – 2J – k and B = 4T – 2J + 4k (5 marks)

A:

Q: For what values of t and s does the equality (- (2t + 2), 3s + t) = (2s + 4t, 7t – 4) hold true? t =…

A: see below the answer and calculation Equating both sides means the components are equal

Q: Let Ā = -(1+ m)î + 7j – 5k , B = xî + (6 + n)j – 2k and Ĉ = (8+ m)î – 2k , find the following: If…

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

Q: 10. In the diagram, M is the mid-point of CD, BP:PM = 2:1, AB AD = z. = x, and AC = y and %3D…

A: Given that:                               NOTE: As per our answering guidelines, we can only answer…

Q: Given v = 3i - 2j, w = 2i + j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: Given that, The vectors  v = 3i - 2j, w = 2i + j. We have to find projw v By using a formula, projw…

Q: Q2/ If A=ai+bj+3k, B= 2i+3j+4k, C-i+j+6k are vectors , perpendicular to B and A is perpendicular to…

A:

Q: If c = 14, is the vector 2i + 5j in the span of ci – 12j and 7i - 6j? If c # 14, is the vector 2i +…

A: Answer

Q: H.W 6- Determine which of the following vectors are parallel to A = 4i +6j 1. -4i -6j

A:

Q: Q3/the parallelogram is determined but the vectors KL = and KN =, so the area of parallelogram KLMN…

A:

Q: The angle between vector A =4ax+5ay+6az and B = 3ax -2ay + 4az is * O 68.75 degrees O 56.62 degrees…

A: Angle between two vectors

Q: Given v = 6i + 2j and w =i-j, a. Find projwv. b. Decompose v into two vectors v, and V2, where v, is…

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.