The Figure Formed By Four Points Ijk 2i3j 3i5j2k Kj Is A
1) parallelogram 2) rectangle 3) trapezium 4) square Answer: (3) Trapezium Solution: Suppose, PQ = i+2j+k QR = i+2j-2k RS... View Article
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Three Non Zero Collinear Vectors A B And C Are Such That A 3b Is Collinear With 3b 2c Is Collinear
1) 0 2) 2a 3) 3b 4) 4c Answer: (1) 0 Solution: Given, Three non – zero collinear vectors a,... View Article
If 3i2j6k Is A Unit Vector Then The Values Are
1) ± 1/7 2) ± 7 3) ± √43 4) ± 1/√43 5) ± 1/√7 Answer: 1) ± 1/7 Solution:... View Article
If A Is Vector Perpendicular To Both B And C Then
1) a + (b + c) = 0 2) a × (b + c) = 0 3) a × (b... View Article
U I X A X I J X A X J K X A X K Is Equal To
1) a 2) 2 a 3) 3a 4) None of these Answer: (2) 2a Solution: Given, u = i x... View Article
If Aijk Bij Ci And Axbxc A B Then The Value
1) 0 2) 1 3) 2 4) 3 Answer: (1) 0 Solution: Given, a=i+j+k, b=i+j, c=i (axb)xc = (a.c)b –... View Article
The Value Of I X J X K J X K X I K X I X J Is
1) 0 2) \(\begin{array}{l}\hat{i}\end{array} \) 3) \(\begin{array}{l}\hat{j}\end{array} \) 4) \(\begin{array}{l}\hat{k}\end{array} \) Answer: (1) 0 Solution: i x (j + k)... View Article
The Point Collinear With 1 2 3 And 2 0 0 Among The Following Is
1) (0, 4, 6) 2) (0, –4, –5) 3) (0, –4, –6) 4) (0, –4, 6) Answer: (3) (0, –4,... View Article
If A Lambda B B Lambda C C A Lambda Abc2 Then Lambda Is Equal To
1) 0 2) 1 3) 2 4) 3 Answer: (2) 1 Solution: Taking LHS, [a×b b×c c×a] = (a×b).((b×c)×(c×a)) As... View Article
If A2i3jk Bi2j4k And Cijk Then What Is The Value Of Axbaxc
1) 47 2) 74 3) –74 4) None of these Answer:(3) -74 Solution: Given, a=2i+3j-k, b=-i+2j-4k and c=i+j+k = -42... View Article
If The Vectors Aijk Ibjk Ijck Abc 1 Are Coplanar Then The Value Of 11a11b11c Is
1) –1 2) 0 3) 1 4) ½ Answer: (3) 1 Solution: Given, vectors ai+j+k, i+bj+k, i+j+ck (a,b,c ≠1) are... View Article
Let A B And C Be The Distinct Nonnegative Numbers If The Vectors Aiajck Ik And Cicjbk Lie In A Plane Then C Is
1) the harmonic mean of a and b 2) equal to zero 3) the arithmetic mean of a and b... View Article
Let A B And C Be Noncoplanar Vectors If A2b2bc5ca Lambda Abc Then Find Lambda
1) 10 2) 11 3) 12 4) 0 Answer: (3) 12 Solution: Given, [a+2b 2b+c 5c+a]=λ[abc] \(\begin{array}{l}\left[\begin{array}{lll} 1 & 2... View Article
If A Ik B Xij1xk And C Yixj1xyk 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... View Article
The Volume In Cubic Unit Of The Tetrahedron With Edges Ijk Ijk And I2jk Is
1) 4 2) 2/3 3) 1/6 4) ⅓ Answer: (2) ⅔ Solution: Given the edges of tetrahedron are i+j+k, i-j+k... View Article
If The Points Whose Position Vectors Are 2ijk 6ij2k And 14i5jpk Are Collinear Then The Value Of P Is
1) 2 2) 4 3) 6 4) 8 Answer: (2) 4 Solution: Given the three vectors 2i+j+k, 6i-j+2k and 14i-5j+pk... View Article
If Abc Are Noncoplanar Vectors And Lambda Is A Real Number Then Ab2bcabcb For
1) exactly two values of λ 2) exactly three values of λ 3) no real value of λ 4) exactly... View Article
If The Vectors Aiaja2k Bibjb2k And Cicjc2k Are Three Noncoplanar Vectors And Determinant
1) 0 2) 1 3) 2 4) –1 Answer: (4) -1 Solution: As per the given condition, vectors a,b and... View Article
If The Vectors 2i3j4k And I2jk And Mij2k Are Coplanar Then The Value Of M Is
1) 5/8 2) 8/5 3) – (7/4) 4) ⅔ Answer: (2) 8/5 Solution: Given the three vectors, a = 2i-3j+4k... View Article
If Alpha Is A Root Of 25 Cos Square Theta 5 Cos Theta 12 0
1) 24/25 2) -24/25 3) 13/18 4) -13/18 Answer: (2) -24/25 Solution: Given, α is a root of 25 cos2θ... View Article
