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
To find the value of t such that vectors a and b are perpendicular, we use the condition that their dot product must be zero (a · b = 0). Step 1: Write down the given vectors. a = 2i - 5j + k b = -3i + tj - 7k Step 2: Calculate the dot product a · b. The dot product is found by multiplying the corresponding components and summing them. a · b = (2)(-3) + (-5)(t) + (1)(-7) Step 3: Set the dot product equal to zero and solve for t. -6 - 5t - 7 = 0 -13 - 5t = 0 -5t = 13 t = -(13)/(5) The value of t for which the vectors are perpendicular is -(13)/(5). Send me the next one 📸