Prove that for every pair of vectore XERn and YER's llocl·llyll.cosd where I is the angle between x and andy

Q: list the elements of the subgroup generated by the subset {18, 24, 39} of Z

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Q: For questions with enumerated functions, tell whether they are linearly dependent or linearly…

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Q: Find the value of x so that the vector i+2j+xk   makes and angle  pi/4  of  with the positive…

A: i+2j+xkTo Find: Value of x so that the vector makes an angle of π4 with the positive z axis.

Q: 2. Find the exact angle between vectors a = 3 î - j - 2k – 18 10 b = v – w, wherev = 2î + ĵ + 4kandŵ…

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Q: 1. Let = =(3, 2, 1) and 5 = (-4,3₁-1) e) Evaluate (3a+46) (3a - 4b). f) Find the angle between a and…

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Q: 6. If A = a₁i + a₂j + azk is a constant vector, and if R = xi + yj + zk and R = |R| show that V. AXR…

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Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: 8. The magnitude of force F is 450 lb. Express F in Cartesian vector form. y, ft 030° A(4,-2) -x, ft

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Q: Let = ondu= a. Compute (ul. b. Compute +7. c. Compute 3u- 2 d. Compute e. Find o vector…

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Q: If f(x, y) = 2x² + 5y² and u is the unit vector in the direction of T which of the following…

A: Given f(x,y)=2x2+5y2 u⇀ is the the unit vector in the direction of π6. So,  u⇀=cosπ6,sinπ6=32,12

Q: If A-(rsinOcos -cos2Osin

A: Given, At the point , we have determine the vector component of that is parallel to vector .

Q: 2. The position vectors of A, B and C relative to a fixed origin O are respectively, Find, ABAC

A: [2].

Q: 4. [6.1] If vector b is shown below, sketch a vector. a) Equal to b b) Opposite to b c) With the…

A: Solution of given question is written in below steps.

Q: find the compoment form of vector v given ||v|| = 13 and the angle with positive axis is theta=300…

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Q: Quolel X= -gi +sj -K, Y. i-2 k yo i-2 K Find X x Y

A: (1) Consider the given vectors x=-2i+3j-k and y=i-2k   We have to find x×y   Now, x×y=ijk-2   3-11 0…

Q: The scalar product of two vectors is defined as the product of their magnitudes times the of the…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: Let v = ai + bj. Show that v/lvl is a unit vector in the direction of v.

A: Consider the following vector: v→=ai^+bj^ Magnitude of vector v→: v→=a2+b2…

Q: Given point Al-4, -5, 8) and point B(3, 0, 6). let be the position vector from the origin to point A…

A: Given;           Origin:0,0,0Point A: -4,-5,8Point B:3,0,6 Position vector…

Q: cos 0, i + sin 01j and u2 = cos 02 i + sin 02j where i, j are the Cartesian unit vectors. Find the…

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Q: If u is a unit vector find the dot product of vectors u and w

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