A rigid body is acted on by two forces, R =ai +bj - 3 at the point (1,2,-1) and F =i+aj+bkat the point (-1,0,1). If the force system is equipolilent to the force F and the couple G, which have no components along i then determine F.

Q: Let B be a subset of R4. Which of the following statements are correct? If |B| = 5, then B spans R4…

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Q: Calculate v × w. v = 〈2, 0, 0〉, w = 〈-1, 0, 1〉

A: Given vectors are v=2, 0, 0 and w=-1, 0, 1. To calculate: v×w Solution: Given vectors can be written…

Q: Find u · v. u - (7, 2) - (-6, 3) V u.v -

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Determine whether the argument is valid or invalid. You may compare the argument to a standard form…

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Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

A: Given query is to find the value of k.n

Q: would two independent vectors span a plane whereas two dependent vectors span a line?

A: If two vectors are linearly dependent:

Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

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Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: If u = -i + 4j - 7k and v = 5i - 2j - 9k calculate the product of u . v  u . v =

A: Use the dot product for finding the product of vector .

Q: The forces F, = (-8, 1) and F, = (5, 6) act on an object. Find the resultant force, R.

A: The resultant force is the net force of all the forces, which is the result of adding all the forces…

Q: 4. a) b) Let x = 27 + 3j - k, y = i- j + 4k and Z = −3ỉ + ]. Express the vector x – ỷ – 3ž in terms…

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Q: what values ofh Is V3 ea4 (9) lineasly dlependnt? values of h is {v, VzNs} Justiky answer tined - 2…

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Q: Let V1 = 2 V2 = 0 2 V3 = 2 V4 = 3 Decide the dependence or independence of the vectors {V₁, V2, V₁}…

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Q: Q3/ Let å = (2,1, -4) and b = (3,-2,5) be two vectors. Find a vector that perpendicular to both å…

A: Q3/ The given vectors are a⇀=2,1,-4 and b⇀=3,-2,5

Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

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Q: If a = i+ 8j + k and b = i+ 13j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: Express the following as a linear combination of u (2, 1, 5), v (1,-1, 4) and w = (6, 8, 6). (9, 14,…

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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.