class test-vector analysis

Physics Department, Panskura Banamali College by Dr. Abhijit Kar Gupta Physics Hons., 1 st Year : Surprise Test-2006 on Vector Analysis (Tick the correct answer) 1. If the two vectors are k j i A ) ) ) + + = 4 3 and k j i B ) ) ) + − = then (a) they are orthogonal, (b) orthonormal (c) anti-parallel, (d) none of these 2. The directional derivative of 2 2 ) , ( y x y x f + = at (1,1) along j i u ˆ 2 3 ˆ 2 1 ˆ + = is (a) 2 3 2 + , (b) 0, (c) 3 1 + (d) 1 3. If r 1 = φ , then φ 2 ∇ is (a) 1, (b) -1, (c) 0, (d) 2 1 r 4. = × ∇ 2 r r ? (a) r , (b) 0, (c) r − , (d) r ) 5. For a particle moving in a circular orbit t r j t r i r ω ω sin cos ) ) + = , the value of dt r d r × is (a) r i ω ) , (b) 2 r k ω ) , (c) 2 r j ω ) , (d) 2 2 r j r i ω ω ) ) + 6. If we have a force j x i y F ) ) + = , then the work done along a circular path in the xy- plane from 0 = θ to 2 π θ = is (a) π , (b) 2 π , (c) 0, (d) 1 7. If r V × = ω , and ω is a constant vector then V × ∇ =? (a) ω , (b) ω 2 , (c) ω − , (d) 0 8. The vector 3 r r is (a) irrotational, (b) solenoidal, (c) both irrotational and solenoidal, (d) none of these 9. If a is a constant vector and r is the radius vector then ( ) = × × ∇ r a ? (a) a , (b) 2 a , (c) 0, (d) r 10. Find the angle between two vectors a and b if b a b a ⋅ = × (a) 30 o , (b) 0, (c) 45 o , (d) 90 o

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Class Test on Vector Analysis. Multiple Choice type.

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Physics Department, Panskura Banamali College by Dr. Abhijit Kar Gupta

Physics Hons., 1st Year : Surprise Test-2006 on Vector Analysis (Tick the correct answer) 1. If the two vectors are kjiA

)))++= 43 and kjiB

)))+−= then

(a) they are orthogonal, (b) orthonormal (c) anti-parallel, (d) none of these

2. The directional derivative of 22),( yxyxf += at (1,1) along jiu ˆ23ˆ

21ˆ += is

(a) 2

32 + , (b) 0, (c) 31+ (d) 1

3. If r1

=φ , then φ2∇ is

(a) 1, (b) -1, (c) 0, (d) 2

4. =

×∇ 2rr ?

(a) r , (b) 0, (c) r− , (d) r)

5. For a particle moving in a circular orbit trjtrir ωω sincos))

+= , the value of dtrdr × is

(a) riω)

, (b) 2rkω)

, (c) 2rjω)

, (d) 22 rjri ωω))

+ 6. If we have a force jxiyF

))+= , then the work done along a circular path in the xy-

plane from 0=θ to 2πθ = is

(a) π , (b) 2π , (c) 0, (d) 1 7. If rV ×= ω , and ω is a constant vector then V×∇ =? (a) ω , (b) ω2 , (c) ω− , (d) 0

8. The vector 3rr is

(a) irrotational, (b) solenoidal, (c) both irrotational and solenoidal, (d) none of these 9. If a is a constant vector and r is the radius vector then ( )=××∇ ra ?

(a) a , (b) 2a , (c) 0, (d) r 10. Find the angle between two vectors a and b if baba ⋅=×

(a) 30 o , (b) 0, (c) 45 o , (d) 90 o

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