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Question: The vector with terminal point C(2,-4,7) and initial point D(1,3,-8) is :...

The vector with terminal point C(2,-4,7) and initial point D(1,3,-8) is :

A

i^−7j^+15k^\hat{i} - 7\hat{j} + 15\hat{k}

B

−i^−9j^+15k^-\hat{i} - 9\hat{j} + 15\hat{k}

C

i^+5j^−6k^\hat{i} + 5\hat{j} - 6\hat{k}

D

3i^+4j^+2k^3\hat{i} + 4\hat{j} + 2\hat{k}

Answer

i^−7j^+15k^\hat{i} - 7\hat{j} + 15\hat{k}

Explanation

Solution

To find the vector with a given terminal point CC and initial point DD, subtract the coordinates of the initial point DD from the coordinates of the terminal point CC.

Given:

  • Terminal point C(2,−4,7)C(2, -4, 7)
  • Initial point D(1,3,−8)D(1, 3, -8)

The vector DC→\overrightarrow{DC} is calculated as follows:

DC→=C−D=(2−1)i^+(−4−3)j^+(7−(−8))k^\overrightarrow{DC} = C - D = (2-1)\hat{i} + (-4-3)\hat{j} + (7-(-8))\hat{k} =1i^−7j^+15k^= 1\hat{i} - 7\hat{j} + 15\hat{k}

Therefore, the vector is i^−7j^+15k^\hat{i} - 7\hat{j} + 15\hat{k}.