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If A Is Perpendicular To Both B And C Then

1) a.(b x c) = 0 2) a x (b x c) = 0 3) a x (b+c) = 0 4) a+(b+c) = 0 Answer: (2) a x (b x c) = 0 Solution: Given, a is perpendicular to both... View Article

The Vectors Which Isare Coplanar With Vectors Ij2k And I2jk Are Perpendicular To The Vector

1) j-k 2) -i+j 3) i-j 4) -j+k Answer: Both (3) i-j and (4) -j+k Solution: Let a = i+j+2k and b= i+2j+k c = i+j+k Let the vector on the... View Article

If A B And C Are Unit Vectors Such That A X B X C 1 2 Then Angle Between A And C Is

1) π/6 2) π/4 3) π/2 4) π/3 Answer: (4) π/3 Solution: Given, a x (b x c) = ½b (a.c)b - (a.b)c = ½ b If we compare both the sides, a.c =... View Article

If A B And C Are Unit Coplanar Vectors Then 2a B 2bc 2ca Is Equal To

1) 1 2) 0 3) –√3 4) √3 5) 6 Answer: (2) 0 Solution: Given [a b c] = 0 Now, [2a – b 2b – c 2c – a] = (2a – b).{(2b – c) × (2c – a)} = (2a... View Article

Let A B And C Be The Distinct Nonnegative Numbers If The Vectors Lie In Plane Then C Is

1) the harmonic mean of a and b 2) equal to zero 3) the arithmetic mean of a and b 4) the geometric mean of a and b Answer: Solution: Given,... View Article

The Value Of Ab Bc Ca Is

1) 0 2) 1 3) 2 4) None of the above Answer: (1) 0 Solution: Since, a−b+b−c+c−a=0 Vectors a−b,b−c and c−a are coplanar, therefore [a−b b−c c−a]=0... View Article

If A And B Unit Vectors Such That A B C 1 4 Then Angle Between A And B Is

1) π/3 2) π/4 3) π/6 4) π/2 5) π/12 Answer: (3) π/6 Solution: [a × b, a × b] = 1/4 (a × b).(a × b) = 1/4 |a x b|2 = ¼ |a x b| = ½ a b... View Article

If Aij Bjk Cki If D Is A Unit Vector Such That Ad 0 B C D Then D Is Are Equal To

1) ±(i+j-k)/√3 2) ±(i+j-2k)/√6 3) ±(i+j+k)/√3 4) ±k 5) i+j Answer: (2) ±(i+j-2k)/√6 Solution: Given, [b c d] = 0 So, b,c and d are... View Article

If A Ik B Xij1xk And Cyixj1xyk Then A B C Depends On

1) neither x nor y 2) both x and y 3) only x 4) only y Answer: (1) neither x nor y Solution: Given, a = i-k, b = xi+j+(1-x)k and... View Article

If Ab And C Are Three Noncoplanar Vectors Then Abcab Ac Equals

1) 0 2) [A, B, C] 3) 2[A, B, C] 4) -[A, B, C] Answer: (4) -[A, B, C] Solution: (A+B+C).[(A+B)×(A+C)] =(A+B+C).(B×A+A×C+B×C) [Expansion]... View Article

If A Is Perpendicular To B And C A 2 B 3 C 4 And The Angle Between B And C Is 2pi3 Then A B C Is Equal To

1) 4√3 2) 6√3 3) 12√3 4) 18√3 Answer: (3) 12√3 Solution: Given, |a|= 2, |b| = 3, |c| = 4 since a ⊥ b and a⊥c, so |a b c| = a. (b x c) =... View Article

The Number Of Distinct Real Values Of For Which The Vectors 2ijk I2jk And Ij2k Are Coplanar Is

1) zero 2) one 3) two 4) three Answer: (3) Two Solution: Given three vectors are coplanar, therefore, λ6 -3λ2 - 2 = 0 (1+λ2)2 (λ2 -2) =... View Article

Three Vectors 7i11jk 5i3j2k And 12i8jk Forms

1) an equilateral triangle 2) an isosceles triangle 3) a right angled triangle 4) collinear Answer: (3) a right angled triangle Solution:... View Article

If The Volume Of The Parallelepiped With A X B B X C C X A As Coterminous Edges Is 8 Cubic Units

a) 8 cubic units b) 512 cubic units c) 64 cubic units d) 24 cubic units Answer: (c) 64 cubic units Solution: Given, Volume1 = [a x b, b x... View Article

If Ai 4 Then A J X2j 3k Is Equal To

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

The Vector A I 2j K Lies In The Plane Of The Vectors B Ij And C Jk And Bisects The Angle

1) α = 1, β = 1 2) α = 2, β = 2 3) α = 1, β = 2 4) α = 2, β = 1 Answer: (1) α = 1, β = 1 Solution: Given, vector a = αi + 2j + βk lies in... View Article

The edges of a parallelopiped are of unit length and are parallel to non – coplanar unit vectors a, b, c such that a.b = b.c = c.a = ½. Then, the volume of the parallelopiped is? (1) 1/√2 cu unit (2) 1/2√2 cu unit (3) √3/2 cu unit (4) 1/√3 cu unit

Answer: (1) 1/√2 cu unit In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms. Any of the three pairs of... View Article

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