Tiêu đề 00. VECTORS.pdf ✅

PAPER 1 (1.) Given that ˆ ˆ PQ Q P = , which of the following relation is not correct : (1) P Q= (2) ˆ ˆ P Q= (3) P Q= (4) ˆ ` P Q P Q . . = (2.) Given that two vector ˆ ˆ ˆ A i j k = − + and ˆ ˆ B i j k =+− . Find the angle between two vector A and B (1) 1 1 Cos 4 −       (2) 1 1 Cos 3 −     −   (3) 1 1 Cos 5 −       (4) 1 1 Cos 7 −       (3.) Find the component of ˆ ˆ a i j = + 2 3 along the direction of vectors ˆ ˆ     +   i j : (1) ˆ ˆ 5 2 i i     +   (2) ˆ ˆ 3 2 i i     +   (3) ˆ ˆ 5 2 i j   − +     (4) ˆ ˆ 3 2 i j   − +     (4.) Find the area of the formed by the triangle tips of the vector ˆ ˆ ˆ ˆ ˆ a i j k b i j k = − − = − + 3 , 4 3 and ˆ ˆ ˆ c i j k = − + 3 2 (1) 5.6 sq. unit (2) 6.4 sq. unit (3) 6.9 sq.unit (4) 6.5 sq. unit (5.) Two vector A and B are such that A B C + = and A B C + = then the vector A and B are: (1) Parallel (2) Perpendicular (3) Anti-parallel (4) Null vector (6.) The value of ( A B A B +  − ) ( ) is: (1) 0 (2) 2 A B− (3) A B (4) −  2 A B ( ) (7.) Three Vector AB, and C satisfy the relation A B = 0 and AC. 0 = . The Vector A is parallel to: (1) B (2) C (3) BC. (4) B C (8.) If A B = and A B ⊥ then angle between vector (A + B) and (A B− ) is: (1) 0 (2) 6  (3) 3  (4) 2  (9.) If C A B = + and A C ⊥ and 2 B C = , then find angle between A and B : (1) 6  (2) 3 5  (3) 2 3  (4) 5 6 
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(10.) A and B are two inclined vectors. R is their sum. Choose the correct figure for the given description. (1) (2) (3) (4) (11.) The quantities A x and Ay are called x and y-components of the vector A . Note that A x is itself not a vector, but ˆ Ai x is a vector, and so is ˆ A j y Using simple trigonometry, we can express A x and Ay in terms of the magnitude of A and the angle it makes with the X -axis cos A A x =  sin . A A y =  Choose the correct figure on the basis of given description : (1)
(2) (3) (4) None of these. (12.) A force is inclined at 60 to the horizontal. If its rectangular component in the horizontal direction is 50 N , then magnitude of the force in the vertical direction is : (1) 25 N (2) 75 N (3) 87 N (4) 100 N (13.) Assertion : Vector eddition is commutative Reason : Two vector may be added graphically useing head to tail method or parallelogram method In above question a statement of assertion is followed by statement of reason mark the correct choice. (1) It both assertion and reason arc true and reason is correct explanation of assertion. (2) It both assertion and reason arc true and reason is not correct explanation of assertion (3) assertion is true but reason is false. (4) Both assertion and reason false. (14.) If 1 a and 2 a are two non collinear unit vector and if 1 2 a a + = 3 then the value of ( ) ( ) 1 2 1 2 a a a a −  + 2 is: (1) 2 (2) 3 / 2 (3) 1/ 2 (4) 1