Given that P = (-4/5), q = (1/2) and R = (2/5), find: (i) P + 2R (ii) 3q - P (iii) 2P - q + 3R

Here are the solutions for the given vector operations. Given vectors: P = -4 \\ 5 , Q = 1 \\ 2 , R = 2 \\ 5 i) Find P + 2R Step 1: Substitute the given vectors into the expression. P + 2R = -4 \\ 5 + 2 2 \\ 5 Step 2: Perform the scalar multiplication. P + 2R = -4 \\ 5 + 2 × 2 \\ 2 × 5 = -4 \\ 5 + 4 \\ 10 Step 3: Add the resulting vectors. P + 2R = -4 + 4 \\ 5 + 10 = 0 \\ 15 The answer for (i) is 0 \\ 15 . ii) Find 3Q - P Step 1: Substitute the given vectors into the expression. 3Q - P = 3 1 \\ 2 - -4 \\ 5 Step 2: Perform the scalar multiplication. 3Q - P = 3 × 1 \\ 3 × 2 - -4 \\ 5 = 3 \\ 6 - -4 \\ 5 Step 3: Perform the vector subtraction. 3Q - P = 3 - (-4) \\ 6 - 5 = 3 + 4 \\ 1 = 7 \\ 1 The answer for (ii) is 7 \\ 1 . iii) Find 2P - Q + 3R Step 1: Substitute the given vectors into the expression. 2P - Q + 3R = 2 -4 \\ 5 - 1 \\ 2 + 3 2 \\ 5 Step 2: Perform the scalar multiplications. 2P - Q + 3R = 2 × (-4) \\ 2 × 5 - 1 \\ 2 + 3 × 2 \\ 3 × 5 2P - Q + 3R = -8 \\ 10 - 1 \\ 2 + 6 \\ 15 Step 3: Perform the vector addition and subtraction. 2P - Q + 3R = -8 - 1 + 6 \\ 10 - 2 + 15 2P - Q + 3R = -9 + 6 \\ 8 + 15 = -3 \\ 23 The answer for (iii) is -3 \\ 23 . That's 2 down. 3 left today — send the next one.