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... View Article
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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,... 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... 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 +... 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... 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∣... 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 =... 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... 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... 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 =... 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... 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))... 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 =[(xi+yj+zk).i]i+[(xi+yj+zk).j]j+[(xi+yj+zk).k]k =xi+yj+zk =a
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... 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... 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... View Article
If Abc Are Three Vectors Such That A3 B4 C5 And Abc Are Perpendicular To Bccaab
1) 5√2 2) 6√2 3) 3√2 4) 4√2 Answer: 5√2 Solution: Given, a,b,c are three vectors such that ∣a∣=3,∣b∣=4,∣c∣=5 a,b,c... View Article
If Theta Be The Angle Between The Vectors A2i2jk And B6i3j2k Then
1) cos θ = 4/21 2) cos θ = 3/19 3) cos = 2/19 4) cos θ = 5/21 Answer:... View Article
The Sum Of The Series 6 66 666 Upto N Terms Is
(1) (10n-1 – 9n + 10)/81 (2) 2(10n+1 – 9n – 10)/27 (3) 2(10n – 9n – 10)/27 (4) none... View Article
If The Sum Of Three Terms Of Gp Is 19 And Product Is 216 Then The Common Ratio Of The Series Is
1) -3/2 2) 3/2 3) 2 4) 3 Solution: Let a/r, a, ar be the three terms of GP. Product... View Article
