Consider the points A - B - C - D with position vectors 7- -4- -7k- - - -6- -10k- - - -3- -4k- - 5- - -k- respectively- Then- A B C D is

The correct option is B Rhombus A⃗B⃗= 6î 2ĵ+3k̂ B⃗C⃗= 2î+3ĵ 6k̂ C⃗D⃗=6î+2ĵ 3k̂ D⃗A⃗=2î 3ĵ+6k̂ A⃗B⃗||C⃗D⃗, #160;D⃗A⃗||B⃗C⃗ ...

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Byju's Answer

Standard XII

Physics

Vector Component

Consider the ...

Question

Consider the points $A, B, C, D$ with position vectors $7^i - 4^j - 7^k$ , $^i - 6^j + 10^k$ , $-^i - 3^j + 4^k$ , $5^i -^j +^k$ respectively. Then, $A B C D$ is

S q u a r e

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R h o m b u s

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R e c t a n g l e

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n o n e o f t h e s e

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Solution

The correct option is B $R h o m b u s$
$\to A B = - 6^i - 2^j + 3^k$
$\to B C = - 2^i + 3^j - 6^k$
$\to C D = 6^i + 2^j - 3^k$
$\to D A = 2^i - 3^j + 6^k$
$\to A B | | \to C D, \to D A | | \to B C$
$| \to A B | = 7, | \to B C | = 7, | \to C D | = 7, | \to D A | = 7$
$\to A B . \to B D = 0$
So, quadrilateral is rhombus.

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Similar questions

Q. Consider the points

A, B, C, D

with position vectors

7^i - 4^j + 7^k

^i - 6^j + 10^k

-^i - 3^j + 4^k

5^i -^j +^k

respectively. Then

A B C D

is a

Q. Consider

A, B, C, D

with position vector

7^i - 4^j + 7^k

^i - 6^j + 10^k

-^i - 3^j + 4^k

and

5^i -^j + 5^k

respectively, then

A B C D

is a

Show that the points A,B,C with position vectors $2^i -^j +^k,^i - 3^j - 5^k,$ and $3^i - 4^j - 4^k$ respectively,are the vertices of a right-angled triangle. Hence find the area of the rectangle.

Show that the points A,B and C with position vectors, $a = 3^i - 4^j - 4^k, b = 2^i -^j +^k a n d c =^i - 3^j - 5^k$ respectively, form the vertices of a right angled triangle.

Q. Let

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

and

(^i - 6^j -^k)

be the position vectors of points of points

A, B, C, D

respectively. Then show that

A B ∥ C D

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Consider the points A,B,C,D with position vectors 7^i−4^j−7^k ,^i−6^j+10^k ,−^i−3^j+4^k ,5^i−^j+^k respectively. Then, ABCD is

The correct option is B Rhombus→AB=−6^i−2^j+3^k→BC=−2^i+3^j−6^k→CD=6^i+2^j−3^k→DA=2^i−3^j+6^k→AB||→CD,→DA||→BC|→AB|=7, |→BC|=7, |→CD|=7, |→DA|=7→AB.→BD=0So, quadrilateral is rhombus.

Consider the points $A, B, C, D$ with position vectors $7^i - 4^j - 7^k$ , $^i - 6^j + 10^k$ , $-^i - 3^j + 4^k$ , $5^i -^j +^k$ respectively. Then, $A B C D$ is