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

Drawing a 3-D Shape on a Paper

If the points...

Question

If the points A,B and C have position vectors (2,1,1), (6,-1,2) and (14,-5,P) respectively and if they are collinear, then P =

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
4

$\to O A = 2^i +^j +^k, \to O B = 6^i -^j + 2^k, \to O C = 14^i - 5^j + P^k \Rightarrow \to A B = \to O B - \to O A = 4^i - 2^j +^k, \to A C = \to O C - \to O A = 12^i - 6^j + (p - 1)^k$
A, B, C are collinear $\Rightarrow \to A C = λ \to A B \Rightarrow 12^i - 6^j + (p - 1)^k = λ (4^i - 2^j +^k)$
$\Rightarrow λ = 3, p - 1 = 3 \Rightarrow p = 4.$

Suggest Corrections

Similar questions

If the points A,B and C have position vectors (2,1,1), (6,-1,2) and (14,-5,P) respectively and if they are collinear, then P =

P, Q

R

\to a, \to b

\to c

2 \to a + 3 \to b - 5 \to c = 0

P, Q

R

A, B

C

\to A B = λ \to A C

A, B

C

P, Q

R

\to a, \to b, \to c

2 \to a + 3 \to b - 5 \to c = 0

P, Q, R

A, B, C, - - \to A B = λ - - \to A C

A, B, c

\vec{a} - 2 \vec{b} + 3 \vec{c}, 2 \vec{a} + 3 \vec{b} - 4 \vec{c}

- 7 \vec{b} + 10 \vec{c}

Join BYJU'S Learning Program