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If in the shown parallelogram `bar(AC) = -hat(i) + hat(j) - 3hat(k)` and `bar(BC) = 2 hat(i) + 5 hat(K)` then `bar(BD)` is A. `(5)/(2) hat(i) - (1)/(2) hat(j) + (13)/(2) hat(k)`B. `5hat(i) - hat(j) + 13hat(k)`C. `-5hat(i) + hat(j) - 13hat(k)`D. `-(5)/(2) hat(i) + (1)/(2) hat(j) - (13)/(2)hat(k)` |
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Answer» Correct Answer - B The shown figure is a parallelogram. Then, `bar(AB) + bar(BC) = bar(AC)` ……(i) And `bar(BA) + bar(AD) + bar(AD) = bar(BD)` …..(ii) Also, `bar(AB) = -bar(BA)` and `bar(BC) = bar(AD)` ….(iii) so, from (ii) & (iii) `-bar(AB) + bar(BC) = bar(BD)` ....(iv) Adding (i) & (iv) `2bar(BC) = bar(AC) + bar(BD)` `bar(BD) = 2bar(BC) - bar(AC)` |
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