Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
305 views
in Vectors by (30.0k points)
closed by

If four points A, B, C and D with position vectors 4i + 3j + 3k, 5i + xj + 7k, 5i + 3j and 7i + 6j + k respectively are coplanar, then find the value of x.

1 Answer

+1 vote
by (28.8k points)
selected by
 
Best answer

Formula: -

(iii) Three vectors  \(\vec a,\,\vec b\) and  \(\vec c\)are coplanar if and only if  \(\vec a.(\vec b\times\vec c)=0\)

let position vector of

\(OA=4\hat i+3\hat j+3\hat k\)

position vector of

\(OB=5\hat i+\text x\hat j+7\hat k\) 

position vector of

\(OC=5\hat i+3\hat j\)

position vector of

\(OD=7\hat i+6\hat j+\hat k\)

The four points are coplanar if the vector \(\vec {AB},\vec{AC},\vec {AD}\) are coplanar

⇒ 1(9) – (x – 2)( – 2 + 9) + 4(3) = 0

⇒ 9 – 7x + 14 + 12 = 0

⇒ 35 = 7x

⇒ x = 5

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...