This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems: Question 9: Find the mid-point (M) of AB. To find the position vector of the mid-point M of a line segment AB, we use the formula OM = (1)/(2)(OA + OB). Step 1: Add the position vectors OA and OB. OA + OB = 2 \\ 3 + -4 \\ 5 = 2 + (-4) \\ 3 + 5 = -2 \\ 8 Step 2: Divide the resulting vector by 2 to find the mid-point M. OM = (1)/(2) -2 \\ 8 = (-2)/(2) \\ (8)/(2) = -1 \\ 4 Question a): Find in the form asqrt(b). Given = (1)/(sqrt(5)) and is an acute angle. Step 1: Use the trigonometric identity ^2 + ^2 = 1. Since is acute, will be positive. ^2 = 1 - ^2 ^2 = 1 - ((1)/(sqrt(5)))^2 ^2 = 1 - (1)/(5) Step 2: Calculate the value of ^2 . ^2 = (5)/(5) - (1)/(5) = (4)/(5) Step 3: Take the square root to find . = sqrt((4)/(5)) = sqrt(4)sqrt(5) = (2)/(sqrt(5)) Step 4: Rationalize the denominator to express in the form asqrt(b). = (2)/(sqrt(5)) × sqrt(5)sqrt(5) = 2sqrt(5)5 = (2)/(5)sqrt(5) That's 2 down. 3 left today — send the next one.