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If bisects the angle between and
MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra
Problem If i ^ − 3 j ^ + k ^ \hat{i} - 3\hat{j} + \hat{k} i ^ − 3 j ^ + k ^ bisects the angle between a \mathbf{a} a and − i ^ + 2 j ^ + 2 k ^ -\hat{i} + 2\hat{j} + 2\hat{k} − i ^ + 2 j ^ + 2 k ^ , where a \mathbf{a} a is a unit vector, then
(1) a = 1 105 ( 41 i ^ + 88 j ^ − 40 k ^ ) \mathbf{a} = \frac{1}{105}(41\hat{i} + 88\hat{j} - 40\hat{k}) a = 105 1 ( 41 i ^ + 88 j ^ − 40 k ^ )
(2) a = 1 105 ( 41 i ^ + 88 j ^ + 40 k ^ ) \mathbf{a} = \frac{1}{105}(41\hat{i} + 88\hat{j} + 40\hat{k}) a = 105 1 ( 41 i ^ + 88 j ^ + 40 k ^ )
(3) a = 1 105 ( − 41 i ^ + 88 j ^ − 40 k ^ ) \mathbf{a} = \frac{1}{105}(-41\hat{i} + 88\hat{j} - 40\hat{k}) a = 105 1 ( − 41 i ^ + 88 j ^ − 40 k ^ )
(4) a = 1 105 ( 41 i ^ − 88 j ^ − 40 k ^ ) \mathbf{a} = \frac{1}{105}(41\hat{i} - 88\hat{j} - 40\hat{k}) a = 105 1 ( 41 i ^ − 88 j ^ − 40 k ^ )
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