For non-zero vectors →a and →b if |→a+→b|<|→a−→b|, then →a and →b are
A
collinear
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B
perpendicular to each other
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C
inclined at an acute angle
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D
inclined at an obtuse angle
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Solution
The correct option is D inclined at an obtuse angle Let the angle between →a and →b is α |→a+→b|<|→a−→b| Squaring both side ⇒|→a|2+|→b|2+2|→a||→b|cosα<|→a|2+|→b|2−2|→a||→b|cosα ⇒|→a||→b|cosα<0 ⇒cosα<0