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Question
Find a unit vector in the direction of −−→PQ, where P and Q have coordinates (5, 0, 8) and (3, 3, 2), respectively.
Find a unit vector in the direction of −−→PQ, where P and Q have coordinates (5, 0, 8) and (3, 3, 2), respectively.
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Solution
Since, the coordinates of P and Q are (5, 0, 8) and (3, 3, 2), respectively.
−−→PQ=−−→OQ−−−→OP =(3^i+3^j+2^k)−(5^i+0^j+8^k) =−2^i+3^j−6^k∴ Unit vector in the direction of−−→PQ=−−→PQ|−−→PQ|=−2^i+3^j−6^k√22+32+62=−2^i+3^j−6^k√49=−2^i+3^j−6^k7
Since, the coordinates of P and Q are (5, 0, 8) and (3, 3, 2), respectively.
−−→PQ=−−→OQ−−−→OP =(3^i+3^j+2^k)−(5^i+0^j+8^k) =−2^i+3^j−6^k∴ Unit vector in the direction of−−→PQ=−−→PQ|−−→PQ|=−2^i+3^j−6^k√22+32+62=−2^i+3^j−6^k√49=−2^i+3^j−6^k7
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