Video Transcript
Given that vector 𝐀 is equal to 𝑘, negative four; vector 𝐁 is equal to negative four, 𝑚; and vector 𝐀 is equal to two multiplied by vector 𝐁, determine the values of 𝑘 and 𝑚.
We are told in the question that vector 𝐀 is equal to two multiplied by vector 𝐁. As we also know the components of vector 𝐀 and vector 𝐁, we know that the vector 𝑘, negative four is equal to two multiplied by the vector negative four, 𝑚. We recall that when multiplying a vector by a scalar, we simply multiply each of the components by the scalar.
In this question, we can multiply two by negative four and two by 𝑚. The vector 𝑘, negative four must be equal to the vector negative eight, two 𝑚. For any two vectors to be equal, their individual components must be equal. This means that 𝑘 must be equal to negative eight and negative four must be equal to two 𝑚. Dividing both sides of this equation by two gives us 𝑚 is equal to negative two.
If vector 𝐀 equals 𝑘, negative four; vector 𝐁 equals negative four, 𝑚; and vector 𝐀 is twice vector 𝐁, then the values of 𝑘 and 𝑚 are negative eight and negative two, respectively.
