Question

Find a vector the direction of `bar"a" = hat"i" - 2hat"j"` that has magnitude 7 units.

Answer 1

`bar"a" = hat"i" - 2hat"j"`

`therefore |bar"a"| = sqrt(1^2 + (- 2)^2) = sqrt5`

Unit vector in direction of `bar"a"`

`= hat"a" = bar"a"/|bar"a"| = (hat"i" - 2hat"j")/sqrt5`

∴ vector of magnitude 7 in the direction of `bar"a"` is

`7hat"a" = 7((hat"i" - 2hat"j")/sqrt5) = 7/sqrt5 hat"i" - 14/sqrt5 hat"j"`