3 The parallelogram ABCD shows the points P and Q dividing each of the lines AD and DC in the ratio 1:4 respectively. A P a D Q b a If DA = a and DC = b, express the following in terms of a and b: i AC %3D ii CB bi Find the ratio in which R divides DB. iii DB ii Find the ratio in which R divides PQ.

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

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Q: ctor is a quantity characterized by only a positive or negative number that represents its magnitude…

A:

Q: Use the vectors u = (7,7), v = (-9, 6), and w = (7, -1) to find the indicated quantity. (u.v) - (uw)

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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: Use the given vectors to compute u + v, u-v, and 3u - 4v. u = (3, -7), v= (5, 9) u + v = u - v = 3u…

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Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: 3 -1 V3= 4 3 4 -2 2. 2.

A:

Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

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

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Q: Find area of the triangle with edges (-1,2,4),(1,-2,3),(-2,3,-1)

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

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Q: Find two linearly independent vectors perpendicular to the vector 2 -5 -9 D =

A: Two vectors are said to be perpendicular to each other if and only if their dot product is zero.

Q: How are vectors added and subtracted geometrically? Algebraically?

A: Vector Addition Geometrically:

Q: Using vector algebraic operations. Four vectors drawn from a common point are given as follows: A =…

A: Since the question has multiple subparts, we will answer the first three subparts (a,b,c). If you…

Q: Determine the dot product of the two vectors shown in the diagram. (3.5) 1. -5 4 -2 -11 23 4 5 -2+…

A: Dot product of the given vectors

Q: Give 2 vectors of length 7 that are parallel to (-1, 2, –2).

A: Find the required vectors

Q: 7 Part (b) For each vector q and r, determine if the vector is in the span of the vectors w,, W,,…

A: Given vectors are  w1=1-124w2=230-2, w3=3-516, w4=1630 q=-893-4,r= -76-87

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

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Q: %ャ3y t42 =27 43,3,11> る。1 47 6,6,67

A: Given query is to find the normal vector of the plane.

Q: Find the length of the vector. v = (5, 0, 3, -2) %3D ||v|| = %3D

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.