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
Hey nkemdivo — ready when you are. Q33. Step 1: Identify the given vectors. Let A = 2i - qj - k and B = -2i - 2j + qk. Step 2: Apply the condition for perpendicular vectors. If two vectors are perpendicular, their dot product is zero (A · B = 0). (2)(-2) + (-q)(-2) + (-1)(q) = 0 Step 3: Solve the equation for q. -4 + 2q - q = 0 -4 + q = 0 q = 4 The correct option is B. The scalar q is B. 4. Q34. Step 1: Recall the normal vector to a plane. For a plane given by the equation Ax + By + Cz + D = 0, the vector perpendicular to the plane (normal vector) is N = Ai + Bj + Ck. Step 2: Identify the coefficients from the given plane equation. The equation of the plane is 3x - 5y + z + 7 = 0. Here, A=3, B=-5, and C=1. Step 3: Form the perpendicular vector. The vector perpendicular to the plane is 3i - 5j + 1k. The correct option is B. The vector perpendicular to the plane is B. 3i - 5j + k. Q35. Step 1: Identify the given expression for A. A = ^-1 5 + ^-1 (-3) Step 2: Apply the tangent addition formula. The formula for (x+y) is (x+y) = ( x + y)/(1 - x y). Let x = ^-1 5 and y = ^-1 (-3). Then x = 5 and y = -3. Step 3: Substitute the values into the formula. A = (5 + (-3))/(1 - (5)(-3)) A = (5 - 3)/(1 - (-15)) A = (2)/(1 + 15) A = (2)/(16) A = (1)/(8) The correct option is C. Then A = C. (1)/(8). **