Final answer:
To determine the values of a and b if the vectors a⃗=[a, 26,32] and b⃗=[49,-91, b] are collinear, we can compare the components of the vectors and set up equations. Solving these equations will give us the values of a and b.
Step-by-step explanation:
To determine the values of a and b if the vectors a⃗=[a, 26,32] and b⃗=[49,-91, b] are collinear, we can use the fact that two vectors are collinear if one is a scalar multiple of the other.
To find the values of a and b, we can compare the components of the two vectors. Since the second component of a⃗ is equal to 26 and the second component of b⃗ is equal to -91, we can set up the following equation:
26 = -91 * a
Solving for a, we get:
a = -26/91
Similarly, we can compare the first and third components of the vectors to find the value of b.
Therefore, the values of a and b are a = -26/91 and b = 32/91.