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
Step 1: Recall the condition for perpendicular vectors. Two vectors P and Q are perpendicular if their dot product is zero. P · Q = 0 Step 2: Write down the given vectors. P = 3i - 2j - 4k Q = ni + 2j - k Step 3: Calculate the dot product of P and Q. The dot product of two vectors P = P_x i + P_y j + P_z k and Q = Q_x i + Q_y j + Q_z k is given by: P · Q = P_x Q_x + P_y Q_y + P_z Q_z Substitute the components of P and Q: P · Q = (3)(n) + (-2)(2) + (-4)(-1) P · Q = 3n - 4 + 4 P · Q = 3n Step 4: Set the dot product to zero and solve for n. Since P and Q are perpendicular: 3n = 0 n = (0)/(3) n = 0 The value of n is 0. Send me the next one 📸