Final answer:
To find the magnitude of vector Ċ, we substitute vectors Ả and B into the given equation, solve for Ċ's components, and then use the Pythagorean theorem to calculate the magnitude. The operation involves scalar multiplication and vector addition. The magnitude of a three-dimensional vector is the square root of the sum of its squared components.
Step-by-step explanation:
To find the magnitude of vector Ċ that satisfies the equation 2Ã – 6B + 3℃ = 2ĵ, we first need to express vectors Ả and B in their component form. Given that Ả = î – 2k and B = –ĵ + k/2, we substitute these into the equation, multiplying them by their respective scalars. After simplifying, we solve for the components of vector ℃ and then calculate its magnitude using the Pythagorean theorem on its components.
It's important to note that multiplying a vector by a scalar will affect its magnitude but not its direction, and vector addition follows specific algebraic rules that take into account the individual components of the vectors involved.
For a vector in three dimensions, expressed as Ả = AxÎ + AyĴ + A₂Î, the magnitude can be found using the square root of the sum of squares of its components: |Ả| = √(Ax² + Ay² + A₂²).