The base vectors e; span a three-dimensional space (indices =1, 2 or 3) as shown in the sketch. This is a non-standard coordinate system in which the magnitudes of e, and ez are both 1, but the magnitude of e2 is 2. Also, the angle between e and ę is a/4. The angle between ez and both ei and e2 is a/2. A vector y referred to this basis is given by y = lęj + 1ę2 + 2ę3 a) b) c) Evaluate each of the nine possible values of gij Calculate y · v = Compute y · ę2and use this result to determine the angle between ęzand y

Q: Given vectors u and v in the diagram below, shade in all linear combinations cu + dv for (a) -1 1…

A: (a) Shade the linear combination.

Q: = Complete the following truth table. Use T for true and F for false. You may add more columns, but…

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Q: Determine the vector of magnitude 7 that has the opposite direction of ū = -4î + 13ĵ – 16k.

A: We can find the required vector as below

Q: Consider the basis B of R? consisting of vectors and 5 Find ä in IR? whose coordinate vector…

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Q: Question 1: Given the points P(-9,6) and Q(3,12), state a UNIT vector in the same direction as PO

A: P (-9,6) and Q (3,12)PQ→ = [3 - (-9)]i^ + (12-6)j^PQ→ = 12i^ + 6j^PQ→ = is the vector joing (-9,6)…

Q: If a point A, the position vector ai + bj lies on the line L, vector equations r = 2i +5j +c(i-i),…

A: To find the value of (a), we need to ensure that the position vector of point A, (ai + bj), lies on…

Q: .4 Find the angle between the position vectors to the points (3,-4,0) and (-2, 1, 0) and find the…

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Q: Part C Find the angle b that the vector C makes with vector A. Express your answer in terms of some…

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Q: 2. Find the position vector v for each of the following pairs of points. Point P is the initial…

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Q: Question 3 Find a unit vector in the direction of the given vector. 20 -10

A: 3. To Find: The unit vector in the direction of the vector -2020-10