Given-that-p-2-3-q-4-m-and-r-n-4-If-p-q-r-is-a-unit-vector-find-the-value-of-m-and-n-

Question Number 115793 by ZiYangLee last updated on 28/Sep/20

Given that \underset{∽}{p} = (\begin{matrix} 2 \\ - 3 \end{matrix}), \underset{∽}{q} = (\begin{matrix} - 4 \\ m \end{matrix}) and \underset{∽}{r} = (\begin{matrix} n \\ 4 \end{matrix})

If \underset{∽}{p} + \underset{∽}{q} - \underset{∽}{r} is a unit vector, find the value

of m and n .

Answered by $@y@m last updated on 29/Sep/20

p = 2 i - 3 j

q = - 4 i + m j

r = n i + 4 j

p + q - r = (2 - 4 - n) i + (- 3 + m - 4) j

= (- 2 - n) i + (m - 7) j

∵ p + q - r is a unit vector .

∴∣ p + q - r ∣= 1

\Rightarrow {(- 2 - n)}^{2} + {(m - 7)}^{2} = 1 \dots (A)

I n f i n i t e v a l u e s a r e p o s s i b l e f o r m, n

s a t i s f y i n g (A)

Commented by ZiYangLee last updated on 29/Sep/20

Hmmm \dots

Commented by ZiYangLee last updated on 05/Oct/20

you are right