Find a unit vector in the direction of vector `vecb = hati + 2hatj + 3

1.	Find a unit vector in the direction of vector `vecb = hati + 2hatj + 3hatk`.
Answer» `veca = hati + 2hatj + 3hatk rArr \|veca\| = sqrt(1^(2) + 2^(2) + 3^(2)) = sqrt(14)`. Unit vector in the direction of `veca` is given by `hati = (veca)/(\|veca\|) = ((hati +2hatj + 3hatk))/(sqrt(14)) = ((1)/(sqrt(14)) hati + 2/(sqrt(14)) hatj + 3/(sqrt(14)))`

Discussion

Show that the points `A(1,-2,-8),B(5,0,-2)a n dC(1,3,7)`are collinear, and find the ratio in which `B`divides `A Cdot`
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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)`.