If |→a|=5,|→a−→b|=8 and |→a+→b|=10, then |→b| is equal to :
A
1
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B
√57
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C
13
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D
14
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Solution
The correct option is C√57 |→a|=5,∣∣→a−→b∣∣=8,∣∣→a+→b∣∣=10∣∣→a−→b∣∣2=64|→a|2+∣∣→b∣∣2−2→a⋅→b=64∣∣→a+→b∣∣2=100|→a|2+∣∣→b∣∣2−2→a⋅→b=100∣∣→b∣∣2−2→a⋅→b=39∣∣→b∣∣2+2→a⋅→b=752∣∣→b∣∣2=114∣∣→b∣∣2=57∣∣→b∣∣=√57Hence,correctoptionis(B)