Using vectors show that the points $A (- 2, 3, 5)$ , $B (7, 0, - 1)$ , $C (- 3, - 2, - 5)$ and $D (3, 4, 7)$ are such that AB and CD intersect at the point $P (1, 2, 3)$ .

Open in App

Solution

$\to A B = - 2^i + 3^j + 5^k + t (9^i - 3^j - 6^k)$
$\to C D = 3^i +^j + 7^k + u (6^i + 6^j + 12^k)$
Equating the co ordinates
$- 2 + 9 t = 3 + 6 u \dots (1)$
$3 - 3 t = 1 + 6 u \dots (2)$
$5 - 6 t = 7 + 12 u \dots (3)$
from $(1), (2), (3)$
$⟹ t = \frac{7}{12} u = \frac{1}{24}$ .
substitute in either of equation for point of equation

Suggest Corrections

Similar questions

A (- 2, 3, 5)

B (7, 0, - 1)

C (- 3, - 2, - 5)

D (3, 4, 7)

A B

C D

P (1, 2, 3)

Chords $A B$ and $C D$ of a circle intersect each other at point $P$ such that $A P = C P$ .

Show that : $A B = C D$ .

| - - \to A B | = \frac{1}{2} | - - \to C D | a n d A B | | C D .

¯ ¯¯¯¯¯¯ ¯ A C

¯ ¯¯¯¯¯¯¯ ¯ B D

¯ ¯¯¯¯¯¯ ¯ A B = ¯ ¯¯¯¯¯¯ ¯ B C = ¯ ¯¯¯¯¯¯¯ ¯ C D = \frac{1}{3}

¯ ¯¯¯¯¯¯¯ ¯ A D

Join BYJU'S Learning Program