Final answer:
To determine the values of a and b if the vectors a and b are collinear, set up equations based on the components of the two vectors and solve for a and b.
Step-by-step explanation:
To determine the values of a and b if the vectors a =[a,26,32] and b =[49,−91,b] are collinear, we need to consider the conditions for collinearity. If two vectors are collinear, it means that one vector is a scalar multiple of the other.
Mathematically, if a is collinear with b, then a = kb, where k is a scalar.
In this case, we can write the equation a = kb as [a,26,32] = k [49,−91,b]. Since the vectors are collinear, their corresponding components must be in proportion. Therefore, we can set up the following equations:
- a = kb gives us the equation a = 49k
- 26 = -91k from the second component of the vectors
- 32 = bk from the third component of the vectors
Solving these equations will give us the values of a and b.