The expression 1/√2 (i + j) is a
(A) unit vector
(B) null vector
(C) vector of magnitude √2
(D) scalar
1 Answers
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If `A` and `B` are matrices of the same order, then `A B^T-B^T A` is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix
Let `P=(AB^(T)-BA^(T))` `:. P^(T)=(AB^(T)-BA^(T))^(T)=(AB^(T))^(T)-(BA^(T))^(T)` `=(B^(T))^(T) (A)^(T)-(A^(T))^(T)B^(T)=BA^(T)-AB^(T)` `=-(AB^(T)-BA^(T))=-P` Hence, `(AB^(T)-BA^(T))` is a skew-symmetric matric.
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Let `aa n db` be two real numbers such that `a >1,b > 1.` If `A=(a0 0b)` , then `(lim)_(nvecoo)A^(-n)` is a. unit matrix b. null matrix c. `2l` d. non
Correct Answer - B `A=((a,0),(0,b))` `implies A^(2)=((a,0),(0,b))((a,0),(0,b))=((a^(2),0),(0,b^(2)))` `implies A^(3)=((a^(2),0),(0,b^(2))) ((a,0),(0,b))=((a^(3),0),(0,b^(3)))` `implies A^(n)=((a^(n),0),(0,b^(n)))` `implies (A^(n))^(-1) =1/(a^(n)b^(n)) ((b^(n),0),(0,a^(n)))=((a^(-n),0),(0,b^(-n)))` `implies lim_(n rarr oo) (A^(n))^(-1)=((0,0),(0,0))` as `a gt 1` and `b gt 1`
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If in a system unit of mass is 5kg, unit of length is 10m and unit of time as 5sec, then what will be the value of 1 unit energy in new system.
`[E]=[ML^(2)T^(-2)]=(5)` `=(10)^(2)(5)^(2)=20` joules
2 Answers 2 views
Let `vecV=2hati+hatj-hatk` and `vecW=hati+3hatk`. It `vecU` is a unit vector, then the maximum value of the scalar triple product `[(vecU, vecV, vecW)
Correct Answer - c Given that `vecV = 2hati +hatj -hatk and vecW =hati + 3hatk and vecU` is a unit vector ` |vecU|=1` Now `|vecU vecV vecW] = vecU.(vecV xx...
2 Answers 1 views
Find the magntiude and diraction of the magnitude induction vector `B` (a) of an infinite palne carrying a current of linear density I, the vector `i`
Correct Answer - `B=(1)/(2)mu_(0)j`
2 Answers 1 views
The magnitude of scalar product of two unit vectors perpendicular to each other is
Correct answer is (A) zero
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The magnitude of vector product of two unit vectors making an angle of 60° with each other is
Correct answer is (D) √3/2
2 Answers 1 views
What is the difference between a scalar and a vector?
No. Scalars Vectors i. It has magnitude only It has magnitude as well as direction. ii. Scalars can be added or subtracted according to the rules of the algebra. Vectors are added or subtracted by the geometrical (graphical)...
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If A + B = A - B then vector B must be (A) zero vector (B) unit vector (C) Non zero vector (D) equal to vector A
Correct option is: (A) zero vector
2 Answers 1 views
The magnitude of scalar product of the vectors A = 2i + 5k and B = 3i + 4k is
Correct option is: (C) 26
2 Answers 2 views