2 In the triangle ABC, the point D divides the line AB in the ratio 1:3 and E divides the line AC also in the ratio 1:3. B D a A bE If AD = a and AE= b, prove that: a BC = 4 DE, %3D

Q: 1. Given the vectors l = (2,-6) and 7 = (5, 5) , find %3D a. 37 - 7

A: The given vectors,         u→=2,-6 and v→=5, 5

Q: 1. Parallelogram method Vector A: 10 m, 25⁰ Vector B: 6 m, 15°

A: (1) Given that,   Vector A:  10m,  25o   Vector B:   6m,  15o    Formula: To solve using the…

Q: Consider the following vectors: 1 1 2 ;V2 = 1 Vị = ;V3 4 (a) Determine if these vectors are linearly…

A: Given vector are v1=121, v2=132 and v3=104. (a) We have determine whether the these vectors are…

Q: 1 7 Find if -3w-6(u + 2v) if u = -3j, v = i +2j, and w = -- --. Express your answer as a linear…

A:

Q: 4 9. is 6/2 The distance between the vectors u = and y = -2 %3D -5 True O False

A: Suppose u and v be any vectors from a same vector space. Then the distance between u and v is…

Q: Determine true or false. are linearly independent. True False 1 2 ··· 2 0 -3 The vectors

A: The given statement is                             The vectors 12-3 , 20-1 , 04-5 are linearly…

Q: Find the vector in the direction of ⟨5,−12⟩ with length 3.

A: Given that: Vector is in the direction of <5, -12> and length is 3.

Q: vector (A) = -2 i-5j +2 k vector (B) = -5 i-2j-3 k Find the magnitude of (vector A. vector B)

A:

Q: -5 4 and v = 7 Compute the quantity using the vectors u = 1 u•v V V•v u•v v = (Simplify your…

A: This is a problem of vector calculus. We need the concept of dot product of two vectors to solve the…

Q: Use the given pair of vectors, v= 7i+8j , w= -8j , to find the following quantities. State whether…

A:

Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

A:

Q: vector A = -3 i +6j - 5 k vector B = -2 i + 3j+ k find: (vector A + vector B). (vector A - vector…

A:

Q: Pls help w this ques. Thnk u. Full details in solution...pls explain this so I can understand bettr

A: To understand how the vectors a = [2, 3, −5], b = [8, −4, 3], and c = [−4, 10, −13] are related, we…

Q: Vectors What is the resultant of vectors a and b? ( A C B

A: Given

Q: Show that ā b 12

A:

Q: d a unit vector in the direction of u and in the direction opposite that of u. u = (3,-4) (a) in the…

A:

Q: The magnitude and vector operations.  If v = (5, 3, 1)    and    u= (3, 2, 4)  what is 2|| 2v -…

A:

Q: Vector á = zi+j+zk Vector 6 = i +2j-k áxb-7i-9j-11k Calculate the values of z and z

A: Given that the vectors are:                  a→=xi→+j→+zk→, b→=i→+2j→-k→, and a→×b→=7i→-9j→-11k→. To…

Q: A solar panel is mounted on the roof of a house. The panel may be regarded as positioned at the…

A: If the sum of two angles is a right angle, then the two angles are complementary.

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.