The following three vectors are all in R: A=31-23, B=-3 +4j, d=5i 1. Sketch and label...

 

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The following three vectors are all in R: A=31-23, B=-3 +4j, d=5i 1. Sketch and label all three of these vectors on the appended coordinate grid (and submit it with the rest of this Problem Set) such that the foot of A is at the origin, the foot of B is at the point (-1,1) and the head of C is at the point (2,0). 2. For the three vectors in Problem 1, compute the following: (a) A+ B, -A-B+30 and -12B; (b) The magnitude and direction angle (relative to the positive z-axis, as usual) of -C-A; (c) The dot product -2B. A; (d) The angle between A and C. 3. Let P be the projection of A in the direction of B and Q the projection of A in the direction of C. (a) Find the components of P and Q (b) Find the real numbers p and q such that pP+qQ = A (e) Recall that P points in the same direction as B and in the same direction as C. This means that P bB and Q=cC. Find 6 and c. (d) Using the answers to the previous two problems, determine the linear combination of B and C that gives A. i.e. Finds and t such that sB + tC = A 4. Consider the following R vector: -i+7j-2k. (a) Find the magnitude of it. (b) Determine the angles i makes with the positive r-axis, the positive y-axis and the positive -axis when its foot is at the origin. (e) Find the value of a such that the vector i+aj-2k The following three vectors are all in R: A=31-23, B=-3 +4j, d=5i 1. Sketch and label all three of these vectors on the appended coordinate grid (and submit it with the rest of this Problem Set) such that the foot of A is at the origin, the foot of B is at the point (-1,1) and the head of C is at the point (2,0). 2. For the three vectors in Problem 1, compute the following: (a) A+ B, -A-B+30 and -12B; (b) The magnitude and direction angle (relative to the positive z-axis, as usual) of -C-A; (c) The dot product -2B. A; (d) The angle between A and C. 3. Let P be the projection of A in the direction of B and Q the projection of A in the direction of C. (a) Find the components of P and Q (b) Find the real numbers p and q such that pP+qQ = A (e) Recall that P points in the same direction as B and in the same direction as C. This means that P bB and Q=cC. Find 6 and c. (d) Using the answers to the previous two problems, determine the linear combination of B and C that gives A. i.e. Finds and t such that sB + tC = A 4. Consider the following R vector: -i+7j-2k. (a) Find the magnitude of it. (b) Determine the angles i makes with the positive r-axis, the positive y-axis and the positive -axis when its foot is at the origin. (e) Find the value of a such that the vector i+aj-2k

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Solutions Step 1 1st questions answer The given three vectors are A3i2jB3i4jC5i The foot of A is at ... View the full answer