1.

Write a vector of magnitude 9 units in thedirection of vector `-2 hat i+ hat j+2 hat k`

Answer» Let `veca = -2hati+hatj+2hatk`
Let other vector is `vecb` such that `veca||vecb`
Then, `vecb = lambda veca`, where `lambda` is a scalar.
`=>vecb = lambda(-2hati+hatj+2hatk)`
`=> vecb = (-2lambdahati+lambdahatj+2lambdahatk)`
`=>|vecb| = sqrt(4lambda^2+lambda^2+4lambda^2) = sqrt(9lambda^2)`
`=>|vecb| = 3lambda`
We are given, `|vecb| = 9=> 3lambda = 9 => lambda = 3`
`:. vecb = -6hati+3hatj+6hatk`, which is the required vector.


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