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If A And B Represents The Adjacent Sides Of A Parallelogram Whose Area Is 15 Units Then The Area

1) 45 units 2) 75 units 3) 105 units 4) 165 units Answer: (3) 105 units Solution: Given, if a and b are two adjacent sides of a... View Article

The Vectors A And B Are Not Perpendicular And C And D Are Two Vectors Satisfying B C B D

Answer: (3) c-((a.c)/(a.d))b Solution: The vectors a and b are not perpendicular So, a.b≠0 Given, a.d = 0 b × c = b × d a x (b x c) =... View Article

If A B2 A B2 144 And A 4 Then B Is Equal To

1) 16 2) 8 3) 3 4) 12 Answer: (3) 3 Solution: Given, |a × b|2 + |a ∙ b|2 = 144 Suppose, If angle between a and b is θ, then,... View Article

If A And B Are Vectors Such That A B 29 And A 2i 3j 4k 2i 3j 4k B A Possible Value Of A

1) 0 2) 3 3) 4 4) 8 Answer: (3) 4 Solution: Given, a × (2i + 3j + 4k) = (2i + 3j + 4k) × b a x (2i + 3j + 4k) = -b x (2i + 3j + 4k) (a+b)... View Article

If A B And C Are Three Vectors Such That A B C And B C A Then

1) a ≠ b ≠ c 2) a = b = c 3) a ≠ b ≠ c ≠ 1 4) a, b and c are orthogonal in pairs Answer: 4) a, b and c are orthogonal in pairs Solution: a... View Article

In A Triangle With Vertices A 1 1 2 B5 6 2 And C1 3 1 Find The Altitude N Bd

1) 5 2) 10 3) 5√2 4) 10/√2 Answer: (1) 5 Solution: Given, a triangle with vertices A (1, –1, 2), B(5, –6, 2) and C(1, 3, –1) BD is the... View Article

A B 5 And The Angle Between A And B Is Pi 4 The Area Of The Triangle Constructed On The Vectors A 2b And 3a 2b Is

1) 50 2) 50√2 3) 50/√2 4) 100 Answer (2) 50√2 Solution: Suppose, Area of triangle = ½ (a-2b) x (3a+2b) = (−6(b×a)+2(a×b)) = 8(axb)/2 =... View Article

Let Vector A I 2j K And Vector B I J K Be Two Vectors If Vector C Is A Vector Such That B X C B X A

(1) ½ (2) -1 (3) -½ (4) -3/2 Answer: (3) = -½ Solution: Given, a = i - 2j + k and vector b = i - j + k |a| = √6 |b| = √3 a.b = 4 Now as... View Article

If A B And C Are Unit Vectors Such That Abc0 Then Which Of The Following Is Correct

1) a × b = b × c = c × a = 0 2) a × b = b × c = c × a ≠ 0 3) a × b = b × c = a × c = 0 4) a × b , b × c , c × a mutually perpendicular... View Article

If A I2j2k B 5 And The Angle Between Vector A And B Is Pi6 Then The Area Of The Triangle

1) 15/4 2) 15/2 3) 15 4) 15√3/2 5) 15√3 Answer: (1) 15/4 Solution: Area of triangle = ½ ∣a×b∣ Area = ½ |a||b|sinθ = ½ [3 x 5 x sin π/6]... View Article

If A 1 B 4 Ab 2 And C 2a B 3b Then The Angle Between B And C Is

1) π/6 2) 5π/6 3) π/3 4) 2π/3 Answer: (2) 5π/6 Solution: Given, |a|= 1, |b| = 4, a.b = 2 and c = 2a × b – 3b |a×b|2 = |a|2+|b|2-2(a.b)2... View Article

The Unit Vector Perpendicular To The Vectors Ij And Ij Forming A Right Handed System Is

1) k 2) -k 3) (i+j)/√2 4) (i-j)/√2 Answer: (1) k Solution: Let the unit vector perpendicular to the vectors i-j and i+j is r. Vector r =... View Article

If X Y Z 0 X Y Z 2 And Theta Is Angle Between Y And Z Then The Value Of 2cosec2 3cot2 Is

1) 11/3 2) 8/3 3) 5/3 4) 1 Answer: 11/3 Solution: Given x+y+z=0 y+z=−x |x| = |y| = |z|= 2 ∣y+z∣=∣x∣ |y+z|2 = |x|2... View Article

If A And B Be Two Unit Vectors Such That Angle Between Them Is 60 Then Ab Is Equal To

1) √5 2) √3 3) 0 4) 1 Answer: (4) 1 Solution: |a-b|2 = |a|2+|b|2-2|a| |b| cosθ Given, θ = 60° Therefore, |a-b|2 = |a|2+|b|2-2|a| |b| cos... View Article

If A I2j3k And B 3ij2k Then The Angle Between The Vectors Ab And Ab Is

1) 60° 2) 90° 3) 45° 4) 55° Answer: (2) 90° Solution: Given, a = i+2j-3k b = 3i-j+2k a+b = 4i+j-k a-b = -2i+3j-5k (a+b).(a-b) =... View Article

If Ai4 Then Aj 2j 3k

1) 12 2) 2 3) 0 4) -12 Answer: (4) -12 Solution: Given, a.i = 4 (a.j)×(2j−3k) =a.(j×(2j−3k)) = a.(−3(j×k)) =−3(a.i) (∵j×k=i) =−3(4) =−12... View Article

Aii Ajjakk Is Equal To

1) a 2) 2a 3) 3a 4) 0 Answer: (1) a Solution: Suppose, a=xi+yj+zk So, (a.i)i+(a.j)j+(a.k)k... View Article

The Unit Vector Perpendicular To Ij And Coplanar With I2j And I3j Is

1) (2i-5j)/√59 2) 2i+5j 3) 1/√2(i+j) 4) i+j Answer: (3) 1/√2(i+j) Solution: Let the unit vector be a = xi+yj As per the given condition, a... View Article

A Force Of Magnitude Of 30n Acting Along Ijk Displaces A Particle From A Point 241 To 352 The Work Done

1) 90J 2) 30J 3) 30/√3 J 4) 20J Answer: (2) 30J Solution: As we know, Work done = Force x displacement Displacement = (3i+5j+2k)-(2i+4j+k)... View Article

If A B 1 And A B 3 Then The Value Of 3a 4b 2a 5b Is

1) –21 2) – (21/2) 3) 21 4) 21/2 Answer: (2) -21/2 Solution: Given, |a| = |b| = 1 |a + b| = √3 |a+b|2 = 3 |a|2+|b|2+2ab = 3 1+1+2ab = 3... View Article