Vector d is parallel to vector c, in the same direction and 3 times as long. a) Write d in terms of C. b) Write d as a column vector.

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Vector d is parallel to vector c, in the same direction and 3 times as long. a) Write d in terms of C. b) Write d as a column vector.

Answer 1

To solve this problem, let's follow the steps one at a time: ### Step 1: Determine Vector \(\boldsymbol{c}\) First, we need to determine vector \(\boldsymbol{c}\) based on the information provided. We know the line passes through points (0,6) and (3,11). The vector \(\boldsymbol{c}\) can be found by subtracting the coordinates of the starting point from the coordinates of the ending point: \[\boldsymbol{c} = (3 - 0, 11 - 6) = (3, 5)\] ### Step 2: Write \(\boldsymbol{d}\) in Terms of \(\boldsymbol{c}\) Given that vector \(\boldsymbol{d}\) is parallel to vector \(\boldsymbol{c}\), in the same direction, and 3 times as long, we can express \(\boldsymbol{d}\) in terms of \(\boldsymbol{c}\) as: \[\boldsymbol{d} = 3 \times \boldsymbol{c}\] ### Step 3: Calculate \(\boldsymbol{d}\) Now, substituting the values of \(\boldsymbol{c}\) into the equation for \(\boldsymbol{d}\), we get: \[\boldsymbol{d} = 3 \times (3, 5) = (9, 15)\] ### Final Answer: a) \(\boldsymbol{d}\) in terms of \(\boldsymbol{c}\) is \(\boldsymbol{d} = 3 \times \boldsymbol{c}\). b) \(\boldsymbol{d}\) as a column vector is: \[\boldsymbol{d} = \begin{pmatrix} 9 \\ 15 \end{pmatrix}\]

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Vector d is parallel to vector c, in the same direction and 3 times as long. a) Write d in terms of C. b) Write d as a column vector.

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