Question

A vector= I+j+k , vector c = J-k
Find vector b
Satisfying:-
Vector a*vector b = vector c &
Vector a . Vector b = 3

Answer 1

Answer:

Explanation:

Let b = xi + yj + zk

Now

a.b = x+y+z = 3

Now

a X b = (i+j+k) X (xi +yj +zk) = (z-y)i +(x-z) j + (y-x)k = j- k

Now

z-y = 0, hence z = y

Now

x -z = 1 and y-x = -1

Now

x +y+z = 3

1 +z +z +z = 3

z = 2/3

Hence y = 2/3

x = 5/3

Now

b vector = ( 5i +2j+ 2k)/3

Regards

Answer 2

Explanation:

Let b = xi + yj + zk

Now

a.b = x+y+z = 3

Now

a X b = (i+j+k) X (xi +yj +zk) = (z-y)i +(x-z) j + (y-x)k = j- k

Now

z-y = 0, hence z = y

Now

x -z = 1 and y-x = -1

Now

x +y+z = 3

1 +z +z +z = 3

z = 2/3

Hence y = 2/3

x = 5/3

Now

b vector = ( 5i +2j+ 2k)/3

Regards

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