(a) Let a = (−1, 4, 2, 1), b = (0, 2, 2, 0), c = (-1, 3, 4, 0), d = (-2, 9, 8, 1), and U(a, b, c, d) . (i) Write down a unit vector in the direction of a. (ii) Find the angle between b and c. (iii) Find a subset of {a, b, c, d } which is a basis for U. (iv) State the dimension of U+ (b) Let T = ( 0.3 0.1 0.5 0.6 0.4 0.3 0.1 0.5 0.2 [1] [2] [4] [1] Explain clearly how you know that T is be the transition matrix of a regular Markov chain. [2]

Q: a= b=

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Q: (e) Find the angle between two vectors u = (4, -3, 6) and v = (3, 0, 1).

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Q: Find the vector v = PQ. P = (4,3, 6) Q = (9,5, 3) V =

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Q: Define the points P = (-4, 6) and Q = (2, 4). Find the position vector corresponding to På. %3D %3D…

A: We will find the position vector of PQ as following

Q: Find area of the triangle with edges (-1,2,4),(1,-2,3),(-2,3,-1)

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Q: How long is the shadow cast by a 540-foot tower when the sun's rays follow the vector [6,10,-27]?…

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Q: Let ā = (1, – 5, 2) and b = ( – 1, 5, 3). %3D Find the angle between the vectors (in degrees).

A: We know that for two vectors a→ and b→,   cos(θ)=a⇀.b⇀|a||b|⇀⇀ where θ is the angle between vectors.…

Q: u = (7,2,-5) and v = (9,-1,-6).

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Q: Given vectors a = (-3,1,2), b = (4,0,-8), c = (6,-1,4) find a vector d that satisfies 4a - 2b + 2d =…

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Q: Let ā = (4, 3) and b = (– 4, 4). Find the angle between the vector, in degrees.

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Q: use vectors

A: First, we need to define the vectors AB and AC. We can do this by subtracting the coordinates of A…