Suppose that u and v are orthogonal vectors in R’ of lengths 1 and 2, respectively, and suppose that w E R is parallel to u x v and has length 3. Calculate (u +v+w)·(2u –- v) × (3v – u). Include an explanation of each line in your calculation (i.e. state which properties of the dot and cross products you are using at each stage).

Q: Use Green's Theorem to compute f-y² dx + x²dy over the rectangular curve C shown below. Hint:…

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Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: Consider the points P(5, −2, 3) and q(−3, 0, 2) a. Write vector |op| using unit vectors. b. Write…

A: Basics of VECTOR are used.

Q: - - 1. If à = 2ảx + 6ảy – 3ả₂ and ☎ = −3ảx – 4ảy – 5ả₂, find a. a unit vector in the direction of A…

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Q: If A = 4a, - 6a, + a, and B = 2a, + 5a,, find: (a) A B +2|B (b) a unit vector perpendicular to both…

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Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

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Q: 5. For the vectors = (-3, –4) and v = (-2, 2) Find the dot product u · v, and the angle 0 between…

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Q: Determine the dot product for the two vectors: x = ai+bj+ck and y = di+ej+fk where a = 4, b = 5, c =…

A: Given,

Q: Let i = [-1 4] and j = [-4 1]. Find the following vectors. i = 62 i = -6j = | w = 62 – 6ỹ = = [ -

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Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: d. Find an equation (in point-normal form) of the plane containing the points K, M and N Let R be…

A: This is a question from analytical geometry, 3D geometry, and vector algebra.

Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

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Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: Make all obvious simplifications.

A: We have to solve

Q: A point A(-5,-3) is translated by the vector v = , and then reflected about the line y=0. the…

A: Given that: A(-5, -3) is translated by v=<8, 0>

Q: Given vector u = (-3,2) and v = (-3, –1) , determine the value of v – 2u ir component form.

A: We can determine the component form as below.

Q: Let i = [1 -4] and y = [4 -6]. Find the following vectors. i = 57 ü = 2g =| w = 5i + 2j =||

A: The solution is given below:-

Q: v= (-8,-6) and w=(-12,5) Find the following given: 3v – 2w = а. +w = с. Find the unit vector having…

A: This question is related to vectors, We will solve it using given information.

Q: Find the position vector (i.e. the direction vector) from the point P(−4,−6,3) to the point…

A: To find the position vector (i.e. the direction vector) from the point  P-4, -6, 3 to the point Q4,…

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.