English

If → a = 2 ˆ I + 3 ˆ J + ˆ K , → B = ˆ I − 2 ˆ J + ˆ K and → C = − 3 ˆ I + ˆ J + 2 ˆ K , Find → a → B → C

Advertisements
Advertisements

Question

if  `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`

Sum
Advertisements

Solution

`[vec" a" vec" b" vec" c"]`

= `|(2,3,1),(1,-2,1),(-3,1,2)|`

= 2 (- 4 - 1) - 3 (2+3) + 1 (1 - 6)
= - 30

shaalaa.com
  Is there an error in this question or solution?
2018-2019 (March) 65/1/1

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Let A = `[(0,1),(0,0)]`show that (aI+bA)n  = anI + nan-1 bA , where I is the identity matrix of order 2 and n ∈ N


If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB" = B"A. Further, prove that (AB)" = A"B" for all n ∈ N


If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to ______.


In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.


Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`

 


Investigate for what values of λ and μ the equations
2x + 3y + 5z = 9
7x + 3y - 2z = 8
2x + 3y + λz = μ have
A. No solutions
B. Unique solutions
C. An infinite number of solutions.


If liminii = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where \[A = \begin{bmatrix}l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3\end{bmatrix}\]


Choose the correct alternative.

The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______


Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(5),(4),(-3)]`


Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]`


Identify the following matrix is singular or non-singular?

`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`


Find k if the following matrix is singular:

`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`


If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`


Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A


Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C


Choose the correct alternative:

If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______


AB = AC ⇒ B = C for any three matrices of same order.


If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.


If a matrix A is both symmetric and skew-symmetric, then ____________.


A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are


A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an


If all the elements are zero, then matrix is said to be


How many matrices can be obtained by using one or more numbers from four given numbers?


If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.


If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.


If `A = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.


If A is a square matrix of order 3, then |2A| is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×