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Ab X Ac 2i 4j 4k Then The Area Of Triangle Abc Is

1) 3 sq units 2) 4 sq units 3) 16 sq units 4) 9 sq units Answer: (1) 3 square units Solution: Given, AB x AC = 2i - 4j + 4k Area of... View Article

If The Vectors A B And C From The Sides Bc Ca And Ab Respectively Of A Abcs Then

1) a . b = b . c = c . b = 0 2) a × b = b × c = c × a 3) a . b = b . c = c . a = 0 4) a × a + a × c + c × a = 0 Answer: 2) a × b = b × c = c... View Article

A B2 A B2 Is Equal To

1) a2 b2 2) a2 + b2 3) 1 4) 2 a . b Answer: (1) a2 b2 Solution: (a × b)2 + (a ∙ b)2 Since we know, (a x b) = ab sin θ a.b = ab... View Article

The Magnitude Of Cross Product Of Two Vectors Is Root 3 Times The Dot Product The Angle

1) π/6 2) π/3 3) π/2 4) π/4 Answer: (2) π/3 Solution: As per the given question, if a and b are two vectors, then, |a x b| = √3|a.b|... View Article

If A 10 B 2 And A B 12 Then A Bis Equal To

1) 12 2) 14 3) 16 4) 18 Answer: (3) 16 Solution: Given, |a| = 10, |b|= 2 and a . b = 12 We know that, a.b = |a| |b| cos θ Cos θ =... View Article

Let Aa1ia2ja3k Bb1ib2jb3k And Cc1ic2jc3k Be Three Nonzero Vectors Such That C Is

Let a=a1i+a2j+a3k, b=b1i+b2j+b3k and c=c1i+c2j+c3k be three non-zero vectors such that c is a unit vector perpendicular to both a and b. If the... View Article

If A Ijk B I 3j 3k And C 7i9j11k Then The Area Of Parallelogram Having Diagonals Ab And Bc Is

1) 4√6 units 2) 1/2 (√21) sq units 3) √6/2 sq units 4) √6 units Answer: Solution: Given, a=i+j+k,b=i+3j+5k and c=7i+9j+11k Suppose, a... View Article

Find The Magnitude Of Projection Of Vector 2i3jk On A Vector Which Is Perpendicular To The Plane

1) √3/√2 2) √2/√3 3) 4/√3 4) 2√2/√3 Answer: (1) √3/√2 Solution: Suppose n is the normal vector perpendicular to the plane containing i+j+k... View Article

If U And V Are Unit Vectors And Theta Is The Acute Angle Between Then 2u X 3v Is A Unit Vector For

1) exactly two values of θ 2) more than two values of θ 3) no value of θ 4) exactly one value of θ Answer: (4) exactly one value of θ... View Article

If The Vectors Pq Qr St Tu And Up Represent The Sides Of A Regular Hexagon Then Statement I Statement Ii

1) Statement I is correct, Statement II is correct; Statement II is correct explanation for Statement I 2) Statement I is correct, Statement II... View Article

If A And B Are Any Two Vectors Then 2a 3b 5a 7b A B Is Equal To

1) 0 2) 1 3) a × b 4) b × a Answer: (1) 0 Solution: Given, (2a + 3b) × (5a + 7b) + a × b = 2a x (5a+7b) + 3b x (5a + 7b) + a x b = 10 (a... View Article

The Value Of Axb 2 Ab2 2a2 B2 Is

1) a . b 2) 1 3) 0 4) ½ Answer: (4) ½ Solution: We can write; (a x b)2 = (a x b).(a x b) = (|a| |b| sin θ). (|a| |b| sin θ) = |a|2.|b|2... View Article

A Unit Vector Perpendicular To Both The Vectors Ij And Jk Is

1) (-i-j+k)/√3 2) (i+j-k)/3 3) (i+j+k)/√3 4) (i-j+k)/√3 Answer: (4) (i-j+k)/√3 Solution: Given, unit vector, say c, perpendicular to both... View Article

If A 2 B3 And A B Are Mutually Perpendicular Then The Area Of The Triangle Whose Vertices

1) 5 2) 1 3) 6 4) 8 Answer: (3) 6 Solution: Suppose, A, B and C are the position vectors of vertices 0, a+b and a-b. As we know, Area of... View Article

If B And C Are Any Two Noncollinear Unit Vectors And A Is Any Vector Then Abb Acc Ab Cb Cb C Is

1) 0 2) a 3) b 4) c Answer: (2) a Solution: Let b = i, c = j |b x c| = k = 1 Suppose, vector a = a1i + a2j + a3k a.b = a.i = a1 a.c =... View Article

If Vectora 2b 3c 0 Then Vectora X B B X C C X A Is Equal To

1) 6 (b × c) 2) 3 (b × c) 3) 2 (b × c) 4) 0 Answer: (1) 6 (b × c) Solution: Given, (a + 2b + 3c) = 0 a x b + 2b x b + 3c x b = 0 a x b +... View Article

Let A 2ik Bijk And C4i3j7k If R Is A Vector Such That R X B C X B And Ra 0 Then R Is

1) -i-8j+2k 2) i-8j+2k 3) i+8j+2k 4) None of these Answer: (1) -i-8j+2k Solution: Let R=xi+yj+zk Since R.A=0 ⇒2x+z=0 ....(1) R×B=C×B... View Article

If The Projection Of The Vector A On B Is A B And If 3b Ijk Then The Angle Between A And B Is

1) π/3 2) π/2 3) π/4 4) π/6 5) 0 Answer: (1) π/3 Solution: Given, projection of the vector a on b is |a × b| So, |a x b| = a.( b/|b|) And... View Article

Vectors A And B Are Inclined At An Angle Theta 120 If A 1 2 Then A 3b X 3a B2 Is Equal To

1) 190 2) 275 3) 300 4) 320 5) 192 Answer: (3)300 Solution: Given, θ = 120o If |a| = 1, |b| = 2 [(a + 3b) × (3a + b)]= 3(a x a) - (a x... View Article

If A 5 B 6 And A B 25 Then A X B Is Equal To

1) 25 2) 6√11 3) 11√5 4) 11√6 5) 5√11 Answer: (5) 5√11 Solution: Given, |a|= 5, |b| = 6 and a. b = –25 We can write,... View Article