Name each vector then write the vector in component form. 5. 6.

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Name each vector then write the vector in component form. 5. 6.

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To name and write the vectors in component form based on the given picture details, we need to consider the points through which the line passes. The points given are (0,4) and (1,0).Step 1: Determine the direction of the vectors.Since the slope of the line is negative, the line is decreasing as it moves from left to right. This means that if we consider a vector from (0,4) to (1,0), it will be moving downwards and to the right.Step 2: Name the vectors.We can name the vectors based on their starting and ending points. Let's name the vector that starts at (0,4) and ends at (1,0) as vector 5, and we'll name the vector that starts at (1,0) and ends at (0,4) as vector 6.Step 3: Write the vectors in component form.The component form of a vector is written as <change in x, change in y>.For vector 5 (from (0,4) to (1,0)):Change in x = x2 - x1 = 1 - 0 = 1Change in y = y2 - y1 = 0 - 4 = -4So, vector 5 in component form is <1, -4>.For vector 6 (from (1,0) to (0,4)):Change in x = x2 - x1 = 0 - 1 = -1Change in y = y2 - y1 = 4 - 0 = 4So, vector 6 in component form is <-1, 4>.Answer:Vector 5 in component form is <1, -4>.Vector 6 in component form is <-1, 4>.

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Name each vector then write the vector in component form. 5. 6.

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