Write a vector of magnitude 15 units in the direction of the vector `(

1.	Write a vector of magnitude 15 units in the direction of the vector `(hati -2hatk + 2hatk)`.
Answer» Let `veca = (hati -2hatj + 2hatk)`. Then a unit vector in the direction of `veca` is given by `hata = (veca)/(\|veca\|) = ((hati - 2hatj + 2hatk))/(sqrt(1^(2) + (-2)^(2) + 2^(2))) = 1/3(hati - 2hatj + 2hatk)` . `:.` a vector of magnitude 15 in the direction of `veca`. `= 15 xx 1/3 (hati - 2hatj + hatk) = (5hati - 10 hatj + 10 hatk)`.

Discussion

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Write the different vectors having same magnitude.
Write down the magnitude of each of the following vectors : (i) `veca = hati + 2hatj + 5hatk` , (ii) `vecb = 5hati - 4hatj - 3hatk` (iii) `vecc = (1/(sqrt(3))hati - (1)/(sqrt(3)) hatj + 1/(sqrt(3))hatk)` , (iv) `vecd = (sqrt(2)hati + sqrt(3)hatj - sqrt(5) hatk)`
Find a vector of magnitude 21 units in the direction of the vector `(2hati - 3hatj + 6hatk)`.
Find a vector of magnitude 8 units in the direction of the vector `(5hati - hatj + 2hatk)`.
Find a vector of magnitude 9 units in the direction of the vector `(-2hati + hatj + 2hatk)`.
Find the direction ratios and the direction cosines of the vector joining the points `A(2,1,-2)` and `B(3,5,-4)`.
Find the direction ratios and direction cosines of the vector `veca = (5hati - 3hatj + 4hatk)`.