Show that the points with position vectors $2 space straight i with hat on top space plus space 6 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 7 space straight k with hat on top$ and $3 straight i with hat on top space plus space 10 space straight j with hat on top space minus space straight k with hat on top$ are collinear.

Solution

Let $straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 6 space straight j with hat on top space plus space space 3 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space space 2 straight j with hat on top space plus space 7 space straight k with hat on top comma space space space straight c with rightwards arrow on top space equals space 3 straight i with hat on top space plus 10 straight j with hat on top space minus space straight k with hat on top$ be position vectors of A, B, C respectively.
$AB with rightwards arrow on top space equals space straight P. straight V. space of space straight B space minus space straight P. straight V. space of space straight A space equals space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top$
$equals left parenthesis straight i with hat on top space plus 2 space straight j with hat on top space plus space space 7 space straight k with hat on top right parenthesis space minus space left parenthesis 2 space straight i with hat on top space plus space 6 space straight j with hat on top space space plus space 3 space straight k with hat on top right parenthesis space equals space minus space straight i with hat on top space minus space 4 space straight j with hat on top space plus space 4 space straight k with hat on top$
$BC with rightwards arrow on top space equals space straight P. straight V. space of space straight C space minus space straight P. straight V. space of space straight B space equals space straight c with rightwards arrow on top space minus space straight b with rightwards arrow on top space space space space space space equals space left parenthesis 3 space straight i with hat on top space plus space 10 space straight j with hat on top space minus space straight k with hat on top right parenthesis space space minus left parenthesis straight i with hat on top space plus space 2 space straight j with hat on top space space plus space 7 space straight k with hat on top right parenthesis space equals space 2 space straight i with hat on top space plus space space 8 space straight j with hat on top space minus space 8 space straight k with hat on top$
$therefore space space space space space BC with rightwards arrow on top space equals space minus space 2 space AB with rightwards arrow on top$
$therefore space space space AB with rightwards arrow on top space and space BC with rightwards arrow on top space are space parallel space vectors. But space straight A space is space their space common space point. space therefore space space space space space points space straight A comma space straight B comma space straight C space are space collinear.$

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
(i) 5 seconds
(ii) 1000 cm³(iii) 10 Newton
(iv) 30 km hr
(v) 10 g/cm³(vi) 20 m/s towards north

Classify the following measures as scalars and vectors.
10 kg

Classify the following measures as scalars and vectors.
2 meters north-west

Classify the following measures as scalars and vectors.
40°

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10^–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s²

Classify the following measures as scalars and vectors.
time period

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Show that the points with position vectors and are collinear.

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.(i) 5 seconds (ii) 1000 cm3(iii) 10 Newton(iv) 30 km hr (v) 10 g/cm3(vi) 20 m/s towards north

Classify the following measures as scalars and vectors.10 kg

Classify the following measures as scalars and vectors.2 meters north-west

Classify the following measures as scalars and vectors.40°

Classify the following measures as scalars and vectors.40 watt

Classify the following measures as scalars and vectors.10–19 coulomb

Classify the following measures as scalars and vectors.20 m/s2

Classify the following measures as scalars and vectors.time period