Question

Answer these 2 questions. ( 7 & 8 )

#50 points. NO SPAM. ​

Answer 1

Answer:

7.Given that, 2a -3 b -4c+5d = 0

OR, 2a – 2b – b + c -5c+5d = 0

OR, 2(a-b) – (b –c) -5(c-d) = 0

_ _ _

OR, 2 (BA)= (CB) +5(DC)

i.e. Vector BA can be written as integral multiple of other two vectors (i.e. CB & DC)

so Vectors BA, CB & DC are coplanar, hence the points A, B C, & D.

8.

Answer 2

Explanation :-

To prove :-

Prove that A , B , C and D are coplanar.

Proof :-

According to the question,

$2 \vec{a} \: - 3 \vec{b} \: - 4 \vec{c} \: + 5 \vec{d} \: = 0$

Let position vector of points is

$x \: \vec{a} \: + y \: \vec{b} + z \: \vec{c} + m \: \vec{d} \: = 0$

Comparing the given vectors,

We get,

$x = 2 \: , \: y = - 3 \:, \: z = - 4 \:, \: m = 5$

Let the given vectors are coplanar,

Therefore ,

$\implies \: x + y + z + m = 0$

Substitute the values ,

$\implies \: 2 - 3 - 4 + 5 = 0 \\ \\ \implies \: 7 - 7 = 0 \\ \\ \implies \: 0 = 0$

Hence, we can say that,

$a \:, b \:, c \:, d \: are \: coplanar \:$