Consider Theorem 7.3, given below. If a constant force F is applied to an object, and the resulting movement of the object is represented by the displacement vector d, then the work performed by the force is Work = F. d. The problem that follows is a problem you may have worked previously in Section 2.5. Solve the problem by first expressing the force and the displacement of the object as vectors in terms of the unit vectors i and j. Then use Theorem 7.3 to find the work done. A package is pushed across a floor a distance of 65 feet by exerting a force of 43 pounds downward at an angle of 15° with the horizontal. How much work is done? (Round your answer to the nearest hundred foot-pounds.) ft-lb

Q: The unit vector which is perpendicular to both r1=8ax+3ay- 2az , r2=2ax+7ay-6az is equal to

A: Given, vectors arer1=8ax+3ay-2az, r2=2ax+7ay-6azThe unit vector perpendicular to both vectorsr1, r2…

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = -5i + 7j, V = 6i +…

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Q: and notm ind the unit vector of V= 31 +5j -9k.

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Q: Find in terms of i and j the following vectors :

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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: Find cos(0) if 0 is the angle between the vectors u= 2i + 2j – k and v = 3i + 4k

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Q: Q4/ For the force system shown in Fig. (1), find the forces F1 & F2 (Using Vectors) 30 45 F2 15

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Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

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Q: Suppose we have three distinct unit vectors a, b, andc which satisfy the following equations: (i)…

A: b × c ≠ 0b × c = bc sin θ a^nθ could be anything but θ ≠0 that means b and c are not coplanner…

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Q: Find the positive value of m that makes the angle between the vectors equal to 5 a = i +j+k b = mi –…

A: Given that, a⇀=i^+j^+k^ b⇀=mi^-k^ Then we get, a⇀·b⇀=i^+j^+k^·mi^-k^a⇀·b⇀=m+0-1=m-1 Moreover we get,…

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Q: Let a = 2i – j - 3k and b = 3i – j-k %3D (a) C ) Find two unit vectors orthogonal to both a – i and…

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Q: Sketch the following vectors, and find their components andlengths: i + j + k

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Q: Find the general solution to the following vector DE. 1 æ[t) = | -2 1

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Q: Consider Theorem 7.3, given below. If a constant force F is applied to an object, and the resulting…

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Q: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

Q: Find cos(0) if 0 is the angle between the vectors u= 4i – 3k and v = 2i – 2j + k 2 14 15 15

A: First I have written a short note , just use them and find that  Answer is 1/3

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Q: The angle between the vectors i + 2j + k and 3i+ j - 5k is

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Q: In each part, find the two unit vectors in R² that satisfy the given conditions. 1. The two unit…

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Q: 17) Find a vector v whose magnitude is 26 and whose component in the i direction is twice the…

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Q: Answer 19) (Section 9.7) Find a unit vector orthogonal to both vectors u = 2i +5 j–k v=i+3j-2k Tem…

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Q: Find the unit vector that has the same direction as v = 2i + 2j−k.

A: To find the unit vector for any vector v=ai+bj+ck, the formula v=a2+b2+c2 can be used. This formula…

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A: Consider the given expression as, a-b2

Q: For what value of t, if any, is the vector (4t, -1) parallel to the vector (4, -1)

A: G

Q: Find a unit vector orthogonal to the vector A= 2i-j+k and parallel to the vectors B= 2i+2j and C=…

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Q: Express the following vector as a product of its length and direction: v = 4i + 8j – 16k -

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Q: 4. Find the resultant using (a) the head-to-tail method, and (b) by summing up components. For the…

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A: The given vectors,c01, 212, 110

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Q: The unit vector in the direction of E=6i+8j is 0.3i+4j F

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Q: Solve the following problem using analytical techniques: Suppose you walk 18.5 m straight west and…

A: In right angle triangle by pythagorus we always haveHypotenus=Base2+Height2  and θ=tan-1HeightBase

Q: Find the vector v that has magnitude 3 and makes the angle θ=1/4π with the positive x-axis.

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Q: Express the given vector in terms of the unit vectors i, j, and k. (14, 0, 4)

A: Given,  Vector < 14, 0, 4>

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Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

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Q: Two orthogonal unit vectors x, y E R° such that ||æ – y|| = 2.

A: See the attachment

Q: Given the following vectors, solve for the required.  A = 5i - 9j - 7k B = 6j + 3k +2i C = 4j -…

A: This is a problem of vector calculus, which involves the concept of dot product and cross product.

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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.