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Let a=i+j+k and c=j-k . If b is a vector satisfying a×b=c and a.b=3, then find b.

Let a=i+j+k and c=j-k . If b is a vector satisfying a×b=c and a.b=3, then find b.

Grade:12

2 Answers

Arun
25763 Points
3 years ago
Dear student
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
Arun (askIITians forum expert)
Rishi Sharma
askIITians Faculty 646 Points
9 months ago
Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards

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