If a , ~b , c and d are the pv’s of the point A, B, C and D respectively in three…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{~b}}, \overrightarrow{\mathrm{c}}\) and \(\overrightarrow{\mathrm{d}}\) are the pv’s of the point A, B, C and D respectively in three dimensional space and satisfy the relation \(3 \vec{a}-2 \vec{b}+\vec{c}-2 \vec{d}=0\)then :
- A, B, C and D are coplanar
- the line joining the points B and D divides the line joining the point A and C in the ratio 2 : 1 .
- the line joining the points A and C divides the line joining the points B and D in the ratio 1 : 1 .
- the four vectors \(\vec{a}, \vec{b}, \vec{c} \& \vec{d}\)are linearly dependents.
Answer
(A) A, B, C and D are coplanar, (C) the line joining the points A and C divides the line joining the points B and D in the ratio 1 : 1 ., (D) the four vectors a , b , c d are linearly dependents.
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