If v is any vector and n is any unit vector: (a) Show that v can be expressed as v = (v.) î+ĥx (v × ôn) where the two terms represent components that are parallel and perpendicular to , respectively. (b) Write the equation given above in (a) in index notation.

Q: Find the unit vector in the direction of v = 2i – 5j. You can write your answer either in component…

A: the given vector is  find the norm of the vector  .

Q: If vector A = [4,1] and vector B = [-3,2] and A-B = [-1,-1]  Sketch the computation above and…

A: Given; vector A = [4,1] and vector B = [-3,2]

Q: Let a = 2 (-) (-3). 1 and b = What is a|²|b²+ la · b|²? -2 be two vectors.

A:

Q: Find a unit vector in the same direction as v= (28,-21).

A: A unit vector in the direction of (a, b)

Q: 2. Determine whether the expression is defined or undefined. If it is defined, then determine…

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Q: Answer all question 1- Find the vector equation if the F(t)= cos(41) +3 sin(4)j +1'k at t= (+)²

A: Given vector is rt=cos4ti+3sin4tj+t3k At t=π rt=cos4πi+3sin4πj+π3krt=i+0j+π3k

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?

A:

Q: In the figure, the tip of c and the tail of d are both the midpoint of QR. Express c and d in terms…

A: We have  the tip of c and the tail of d are both the midpoint of QR. Express c and d in terms of a…

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: Use index notation to derive the following vector identities: (a) a (bx c) = b. (cxa) = c (ax b); .…

A: Given information: a→,b→, and c→ are vectors.To…

Q: If vector a= and vector b=, fınd a x b (the cross product of vector a and vector b). Enter the…

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Q: Use the vectors u = (7, 7), v = (-6, 4), and w = (5, -3) to find the indicated quantity. (u · 2v)w…

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Q: Let v vector=[−4 −6] and b vector =[8 1 2] (check the image for reference) Is b vector in the…

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Q: = - A. Find the unit vector that makes an angle (0 with the positive x-axis.

A: The unit vector makes an angle θ=-3π4 with positive x-axis

Q: Choose the equation(s) which have the following resultant vecto K 1 " Select one or more: C. * a.…

A: Given query is to find the resultant vector.

Q: [1 -1 5. Find a vector x + 0 such that 2 | 1 4 = 0. -1] 3 x = 8 1 2 6. Solve for x: 2 2 5 x = 3 07

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Q: For questions 20 and 24, use vectors u = (-4, 1), v = (5,-2), and w (0,6) to perform the indicated…

A: We are given  u=⟨-4, 1⟩v=⟨5, -2⟩w=⟨0, 6⟩ We need to perform the operation given and determine…