Given p = 5 -7 , q = -1 3 , and r = 2 1 .

You're on a roll — Here are the solutions to the vector problems. Question 1: Given p = 5 \\ -7 , q = -1 \\ 3 , and r = 2 \\ 1 . Find 2p - q + r. Step 1: Calculate 2p. 2p = 2 5 \\ -7 = 2 × 5 \\ 2 × -7 = 10 \\ -14 Step 2: Substitute the vectors into the expression and perform the operations. 2p - q + r = 10 \\ -14 - -1 \\ 3 + 2 \\ 1 2p - q + r = 10 - (-1) + 2 \\ -14 - 3 + 1 2p - q + r = 10 + 1 + 2 \\ -17 + 1 2p - q + r = 13 \\ -16 The result is: 13 \\ -16 Question 2: If a = 2i - j and b = i + 3j, what is the vector labelled c? Step 1: Identify the relationship between vectors a, b, and c from the diagram. The diagram shows a parallelogram where a and b are adjacent sides originating from the same point. Vector c is the diagonal originating from that same point. According to the parallelogram law of vector addition, c is the sum of a and b. c = a + b Step 2: Substitute the given vector components and add them. c = (2i - j) + (i + 3j) c = (2+1)i + (-1+3)j c = 3i + 2j The vector c is: 3i + 2j Question 3: Find a unit vector in the opposite direction of v, given vector v = 6i - 8j. Step 1: Calculate the magnitude of vector v. |v| = sqrt(6^2 + (-8)^2) |v| = sqrt(36 + 64) |v| = sqrt(100) |v| = 10 Step 2: Find the unit vector in the direction of v. v = (v)/(|v|) = (6i - 8j)/(10) v = (6)/(10)i - (8)/(10)j v = (3)/(5)i - (4)/(5)j Step 3: Find the unit vector in the opposite direction of v. This is -v. -v = - ( (3)/(5)i - (4)/(5)j ) -v = -(3)/(5)i + (4)/(5)j The unit vector in the opposite direction of v is: -(3)/(5)i + (4)/(5)j Question 4: The image provided cuts off the rest of Question 4. Please send the complete question for me to solve it. Send me the next one 📸