Find the angle between the vectors a=2i+3j+k and b=i - 2j + 3k.
Get the complete, step-by-step math solution for: "Find the angle between the vectors a = 2i + 3j + k and b = i - 2j + 3k.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Recall the formula for the angle between two vectors
The angle θ between two vectors a and b can be found using the dot product formula. This formula relates the dot product of the vectors to the product of their magnitudes and the cosine of the angle between them.
Step 2: Calculate the dot product of the vectors
The dot product of two vectors a=a1i+a2j+a3k and b=b1i+b2j+b3k is given by a1b1+a2b2+a3b3. We substitute the components of the given vectors.
Step 3: Calculate the magnitudes of the vectors
The magnitude of a vector v=v1i+v2j+v3k is given by v12+v22+v32 We calculate the magnitudes for both vectors aandb.
Step 4: Substitute values into the formula and solve for the angle
Now we substitute the calculated dot product and magnitudes into the formula for cosθ After simplifying, we take the inverse cosine to find the angle θ.