Final answer:
To find the value of x so that the two vectors (25,1,12) and ⟨ x, 0,1 ⟩ are orthogonal, we need to set their dot product equal to zero. Solving the resulting equation, x = -12/25.
Step-by-step explanation:
To find the value of x so that the two vectors (25,1,12) and ⟨ x, 0,1 ⟩ are orthogonal, we need to take their dot product and set it equal to zero. The dot product of two vectors is given by multiplying their corresponding components and summing the products. So, (25)(x) + (1)(0) + (12)(1) = 0. Simplifying this equation, we get 25x + 12 = 0. Solving for x, we have x = -12/25.