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17.49 is the magnitude of the resultant vector. This can be obtained by adding the vectors and finding magnitude.
<h3>Calculate the magnitude of the resultant vector:</h3>Resultant vector: vector that gives the combined effect of all the vectors. When we add two or more vectors, the outcome is the resultant vector.
For example,
- Sum of vector (3,4) and vector (5,7)
(3,4) + (5,7) = (3+5,4+7) = (8,11)
(8,11) is the resultant vector of vector (3,4) and vector (5,7)
Magnitude of a vector: the length of the vector. The magnitude of the vector a is denoted as ∥a∥.
Magnitude of a = (a₁, a₂)
∥a∥=
In the given question,
v (8,10) and w (7, -1)
Adding the vectors,
resultant vector = (8,10) + (7, -1) = (15, 9)
Magnitude of a vector (a,b) = √a²+b²
Here, magnitude = √15²+9² = √225+81 = √306 ≈ 17.49
Hence 17.49 is the magnitude of the resultant vector.
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The coefficient matrix is
Its determinant is then
which is equal to 0.