If an object changes its position from point P(5,4,6) to point Q(3,7,9). Calculate displacement vector and its magnitude.

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Solution

$P (5, 4, 6)$ and $Q (3, 7, 9)$

Hence , displacement vector

$\to r = \to P Q = (3 - 5) i + (7 - 4) j + (9 - 6) k$

$⟹ \to r = - 2 i + 3 j + 3 k$

Magnitude of displacement $= r = \sqrt{(- 2)^{2} + 3^{2} + 3^{2}}$

$⟹ r = \sqrt{22}$

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If an object changes its position from point P(5,4,6) to point Q(3,7,9). Calculate displacement vector and its magnitude.

P(5,4,6) and Q(3,7,9)Hence , displacement vector →r=→PQ=(3−5)i+(7−4)j+(9−6)k⟹→r=−2i+3j+3kMagnitude of displacement =r=√(−2)2+32+32⟹r=√22

$P (5, 4, 6)$ and $Q (3, 7, 9)$

Hence , displacement vector

$\to r = \to P Q = (3 - 5) i + (7 - 4) j + (9 - 6) k$

$⟹ \to r = - 2 i + 3 j + 3 k$

Magnitude of displacement $= r = \sqrt{(- 2)^{2} + 3^{2} + 3^{2}}$

$⟹ r = \sqrt{22}$