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M0IITU20 - Vectors qns

# M0IITU20 - Vectors qns - Vectors a b a.b 1 1 2 2 =(B a 2 OA...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. a a a b × + ( ) a a a b . 2 = (A) a a 2 a b 2 (B) a a 2 - a b 2 (C) a a 2 a b 2 (D) None of these 2. The area of a triangle whose vertices are, A (1, - 1, 2), B (2, 1, - 1) and C (3, - 1, 2) is : 13 13 6 (D) 6 3. If a a a b & are two non - zero vectors, then the component of a b along a a is ( ) . . a a a a a a b a b b ( ) . . a a a a a a b b a a ( ) . . a a a a a a b b a b ( ) . . a a a a a a b a a a 4. If a a a a b c + + = 0, then which relation is correct . a a a a b c = = = 0 a a a a a a a b b c c a . . . = = a a a a a a a b b c c a × = × = × 5. If ABCDEF is a regular hexagon and AB AC AD AE AF + + + + = λ AD , then λ = 2 3 4 6 6. If O be the circumcentre and O be the orthocentre of a triangle ABC, then OA OB OC + + = 2 OO 2 O O OO O O 7. If in the given fig. OA a a , OB a b and AP : PB = m : n, then OP = ma n b m n a a + + na mb m n a a + + m a a - n a b n b m n a a - - 8. a a i j k = + + 2 2 3 c c c , i j k = - + + c c c 2 and a c i j = + 3 c c , then + t perpendicular to c if t = 2 4 6 8 9. The area of the parallelogram whose diagonals are, a a i j k = + - 3 2 c c c and i - + c 3 4 is : 10 3 5 3 8 4 10. a a . {( ) × ( + )} = 0 [ ] + [ ] [ ] O P B A Vectors

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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 11. If the vectors 2 3 c c i j - , c c c i j k + - and 3 c c i k - form three concurrent edges of a parallelopiped, then the volume of the parallelopiped is : (A) 8 (B) 10 (C) 4 (D) 14 12. ( ) . a a a a b c × = a a a b a c , if : a . . = 0 . . . . . . . 13. If , , are unit vectors such that + + = 0, then . + . . = 1 3 - 3 2 14. If the position vectors of the points A, B, C be , , 3 - 2 respectively then the points A, B, C are : Collinear Non - collinear Form a right angled triangle None of these 15. If & are the position vectors of A & B respectively, then the position vector of a point C on AB produced such that AC = 3 AB is : 3 a a - 3 - 3 - 2 3 - 2 16. The position vectors of the points A, B & C are c c i j + c c j k + and c c k i + respectively . The vector area of the Δ ABC = ± 1 2 a α , where = (A) - + + c c c i j k c c c i j k - + c c c i j k + - c c c i j k + + 17. If a a = (1, - 1, 1) & = ( - 1, - 1, 0), then the vector satisfying, a a × = a c . = 1, is : (1, 0, 0) (0, 0, 1) (0, - 1, 0) 18. a × = a b × a 0, then for some scalar k : + = k a a + a c + a c = k 19. P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then OA OB OC OD + + + OP 2 OP 3 OP 4 OP 20. A unit vector in the xy - plane which is perpendicular to 4 3 c c c i j k - + (A) c c i j + 2 1 5 (3 4 c c i j + ) 1 5 4 c c i j - ) 21.
3 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 A, B, C, D be 2 3 5 c c c i j k + + , c c c i j k + + 2 3 , - + - 5 4 2 c c c i j k and c c c i j k + + 10 10 respectively, then : (A) AB = CD (B) AB  CD (C) AB CD (D) None of these 22. Let a a = c i be a vector which makes an angle of 120º with a unit vector a b . Then the unit vector ( a a + ) is : (A) - + 1 2 3 2 c c i j - + 3 2 1 2 c c i j 1 2 3 2 c c i j + 3 2 1 2 c c i j - 23. The points with position vectors, 60 3 c c i j + 40 8 c c i j - , a i j c c - 52 are collinear, if a = - 40 40 20 24. If the scalar product of the vector, c c c i j k + + with a unit vector parallel to the sum of the vectors, 2 4 5 c c c i j k + - & λ c c c i j k + + 2 3 be 1,

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M0IITU20 - Vectors qns - Vectors a b a.b 1 1 2 2 =(B a 2 OA...

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