Question

The projection of line joining (3, 4, 5) and (4,6, 3) on the line joining (– 1, 2, 4) and (1, 0, 5) :

• A. 4/3
• B. 2/3
• C. 8/3
• D. 1/3

Answer 1

Answer: (A)

4/3

Answer 2

Direction ratios of joining (–1,2,4) and (1, 0, 5) are

1 + 1, 0 – 2, 5 – 4 = (2, – 2, 1)

\ D.C. of this line are

l = $\frac{2}{\sqrt{4 + 4 + 1}}$ = 2/3

m = $\frac{- 2}{\sqrt{4 + 4 + 1}}$ = – 2/3

n = $\frac{1}{\sqrt{4 + 4 + 1}}$ = 1/3

\ required projection

= $\left| (4 - 3)\frac{2}{3} + (6 - 4)( - 2/3) + (3 - 5)\frac{1}{3} \right|$

= $\left| \frac{2}{3} - \frac{4}{3} - \frac{2}{3} \right|$ = 4/3

& \because projectionoflinejoining(x_{1},y_{1},z_{1})and \\ & (x_{2},y_{2},z_{2})tothelinewhosed.c'sare\mathcal{l},m,nis \\ & |(x_{2}–x_{1})\mathcal{l} + (y_{2}–y_{1})m + (z_{2}–z_{1})n| \end{aligned} \right\}$$