Solve this: Q 150 If the position vectors of three points are a→-2b→+3c→, 2a→+3b→-4c→ and -7a→+10c→, then the three - Maths - Vector Algebra

Question

Solve this:
Q 150 If the position vectors of three points are a → - 2 b
→ + 3 c → ,   2 a → + 3 b → - 4 c
→   a n d   - 7 a → + 10 c → , then the
three points are
(a) collinear
(b) non-collinear
(c) coplanar
(d) None of these

Aarushi Mishra · Accepted Answer

Let poistion vector of Pp→=a→-2b→+3c→Qq→=2a→+3b→-4c→Rr→=-7a→+10c→Let us first assume that these points are collinear
 Then PQR lie in a striaght line
Veector PQ→ must be parallel to QR→ PQ→=q→-p→=2a→+3b→-4c→-a→-2b→+3c→=a→+5b→-7c→ QR→=r→-q→=-7a→+10c→-2a→+3b→-4c→=-9a→-3b→-14c→PQ→ doesn't looks parallel to QR→
 Hence we cannot say they are collinear
Also we cannot commenthat they are non-collinear as a→, b→ and c→ might take values such that PQ→ becomes parallel to PR→
 Since we dont know a→, b→ and c→ hence we cannot commmentBut we know any three points always lie on a plane
 So we can definitely say that they are co-planar

Solve this: Q.150. If the position vectors of three points are a → - 2 b → + 3 c → , 2 a → + 3 b → - 4 c → a n d - 7 a → + 10 c → , then the three points are (a) collinear (b) non-collinear (c) coplanar (d) None of these

Solve this:
Q.150. If the position vectors of three points are $\vec{a} - 2 \vec{b} + 3 \vec{c}, 2 \vec{a} + 3 \vec{b} - 4 \vec{c} a n d - 7 \vec{a} + 10 \vec{c}$ , then the three points are
(a) collinear
(b) non-collinear
(c) coplanar
(d) None of these