A cat is situated at point $A$ (10, 6, -4) and a rat is situated at point $B$ (5, 6, 8). The cat is free to move but the rat is always at rest. The minimum distance travelled by cat to catch the rat is:

5 units

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12 units

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13 units

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17 units

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Solution

The correct option is C 13 units
Given,
Position of a cat $A (10, 6, - 4)$
Position of rat $B (5, 6, 8)$
Position vector, $\to r = (10 - 5)^i + (6 - 6)^j + (8 + 4)^k$
$\to r = 5^i + 0^j + 12^k$
The minimum distance travelled by cat to catch the rat is $| \to r |$ ,
$r = | \to r | = \sqrt{(5)^{2} + (0)^{2} + (12)^{2}} = \sqrt{169}$
$r = 13 u n i t s$
The correct option is C.

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A cat is situated at point A (10, 6, -4) and a rat is situated at point B (5, 6, 8). The cat is free to move but the rat is always at rest. The minimum distance travelled by cat to catch the rat is:

The correct option is C 13 unitsGiven,Position of a cat A(10,6,−4)Position of rat B(5,6,8)Position vector, →r=(10−5)^i+(6−6)^j+(8+4)^k→r=5^i+0^j+12^kThe minimum distance travelled by cat to catch the rat is |→r|,r=|→r|=√(5)2+(0)2+(12)2=√169r=13unitsThe correct option is C.

A cat is situated at point $A$ (10, 6, -4) and a rat is situated at point $B$ (5, 6, 8). The cat is free to move but the rat is always at rest. The minimum distance travelled by cat to catch the rat is: