The points A- B and C with position vectors -2-3-5k- -2-3k- and 7-k- respectively are non collinear-

A⃗= 2î+3ĵ+5k̂, î+2ĵ+3k̂ and 7î k̂ A⃗= 2î+3ĵ+5k̂ B⃗=î+2ĵ+3k̂ C⃗=7î k̂ A⃗B⃗ will be given by O⃗B⃗ O⃗A⃗ =(î+2ĵ+3k̂) ( 2î+3ĵ+5k̂) =3î ĵ 2k̂ A⃗C⃗=O⃗C⃗ O⃗A⃗ =(7î ...

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Byju's Answer

Standard XIII

Mathematics

Test for Collinearity of Points

The points A,...

Question

The points A, B and C with position vectors $- 2^i + 3^j + 5^k,^i + 2^j + 3^k a n d 7^i -^k$ respectively are non collinear.

True

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False

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Solution

The correct option is B False
$\to A = - 2^i + 3^j + 5^k,^i + 2^j + 3^k a n d 7^i -^k \to A = - 2^i + 3^j + 5^k \to B =^i + 2^j + 3^k \to C = 7^i -^k \to A B w i l l b e g i v e n b y \to O B - \to O A = (^i + 2^j + 3^k) - (- 2^i + 3^j + 5^k) = 3^i -^j - 2^k \to A C = \to O C - \to O A = (7^i -^k) - (- 2^i + 3^j + 5^k) = 9^i - 3^j - 6^k = 3 (3^i -^j - 2^k) \Rightarrow \to A C = 3 \to A B$
$\Rightarrow$ AC is parallel to AB with A as a common point. So A, B and C are collinear.

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Similar questions

Q. The points A, B and C with position vectors

- 2^i + 3^j + 5^k,^i + 2^j + 3^k a n d 7^i -^k

respectively are non collinear.

Q. The ratio in which

^i + 2^j + 3^k

divides the join of

- 2^i + 3^j + 5^k

and

7^i -^k

Q. The position vectors of the points

A, B, C

are

2^i +^j -^k,

3^i - 2^j +^k

and

^i + 4^j - 3^k

, respectively. These points

Q. Show that the points

A (- 2^i + 3^j + 5^k), B (^i + 2^j + 3^k)

and

C (7^i -^k)

are collinear.

Q. The position vector of the points

A, B, C

are

(2^i +^j -^k), (3^i - 2^j +^k)

and

(^i + 4^j - 3^k)

respectively. These points

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The points A, B and C with position vectors −2^i+3^j+5^k,^i+2^j+3^k and 7^i−^k respectively are non collinear.

The points A, B and C with position vectors $- 2^i + 3^j + 5^k,^i + 2^j + 3^k a n d 7^i -^k$ respectively are non collinear.