MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Distance Formula

If A2,1, 3, B...

Question

If A(2,1, 3), B(2, -3, 4) , C(-1, 2 , 7) are the three points ; find a point D such that $| - - \to A B | = \frac{1}{2} | - - \to C D | a n d A B | | C D .$

Open in App

Solution

$\begin{matrix} - - \to A B = \frac{1}{2} - - \to C D o r - - \to A B = - \frac{1}{2} - - \to C D - - \to A B = - 4 ˆ j + ˆ k 2 (- 4 ˆ j + ˆ k) = \to D - \to C 2 (- 4 ˆ j + ˆ k) = \to C - \to D - 8 ˆ j + 2 ˆ k - ˆ i + 2 ˆ j + 7 ˆ k = ˆ 0 - 8 ˆ j + 2 ˆ k + ˆ i - 2 ˆ j - 7 ˆ k = ˆ 0 \to D = - ˆ i - 6 ˆ j + 9 ˆ k - ˆ i - 10 ˆ j - 5 ˆ k = - ˆ 0 o r \to D = - ˆ i + 10 ˆ j + 5 ˆ k \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Using vectors show that the points

A (- 2, 3, 5)

B (7, 0, - 1)

C (- 3, - 2, - 5)

D (3, 4, 7)

are such that AB and CD intersect at the point

P (1, 2, 3)

Q. Using vectors show that the point

A (- 2, 3, 5)

B (7, 0, - 1)

C (- 3, - 2, - 5)

D (3, 4, 7)

A B

C D

intersect at the point

P (1, 2, 3)

A = (1, 2, 3), B = (4, 5, 7), C = (- 4, 3, - 6), D = (2, k, 2)

are four points. If the lines

A B

C D

are parallel, then

k =

A = (2, 3, - 1), B = (3, 5, - 3), C = (1, 2, 3), D = (3, 5, k)

are four points. If the lines

A B

C D

are perpendicular, then

k =

A, B, C, D are the points in a vertical line, the lengths AB=BC=CD . If the body Falls from rest at A , prove that the times of describing AB, BC, CD are as 1:√2-√1:√3-√2 .

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Distance Formula

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Distance Formula

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon