(v) बिना अनुमति के किसी अन्य देश के जैव संसाधनों का दोहन कहा जाता है। har intry without being
Answers
Explanation:
EXPLANATION.
Points A B C are the position vectors,
\sf \implies (A) = 3 \hat {i} - y \hat {j} + 2 \hat{k}.⟹(A)=3
i
^
−y
j
^
+2
k
^
.
\sf \implies (B) = 5 \hat {i} - \hat {j} + \hat {k}.⟹(B)=5
i
^
−
j
^
+
k
^
.
\sf \implies ( C) =3x \hat {i} + 3 \hat{j} - \hat {k}.⟹(C)=3x
i
^
+3
j
^
−
k
^
.
\sf \implies \vec {AB} = (5 \hat {i} - \hat {j} + \hat {k} ) - [ 3 \hat {i} - y \hat {j} + 2 \hat {k}] .⟹
AB
=(5
i
^
−
j
^
+
k
^
)−[3
i
^
−y
j
^
+2
k
^
].
\sf \implies \vec {AB} = 5 \hat {i} - \hat {j} + \hat {k} - 3 \hat {i} + y \hat {j} - 2 \hat {k}⟹
AB
=5
i
^
−
j
^
+
k
^
−3
i
^
+y
j
^
−2
k
^
\sf \implies \vec {AB} = 2 \hat {i} - (1 - y ) \hat {j} - 2 \hat {k} .⟹
AB
=2
i
^
−(1−y)
j
^
−2
k
^
.
\sf \implies \vec {BC} = 3X \hat {i} + 3 \hat {j} - \hat {k} - [ 5 \hat {i} - \hat {j} + \hat {k} ] .⟹
BC
=3X
i
^
+3
j
^
−
k
^
−[5
i
^
−
j
^
+
k
^
].
\sf \implies \vec {BC} = 3x \hat {i} + 3 \hat {j} - \hat {j} - 5 \hat {i} + \hat {j} - \hat {k} .⟹
BC
=3x
i
^
+3
j
^
−
j
^
−5
i
^
+
j
^
−
k
^
.
\sf \implies \vec {BC} = (3x - 5) \hat {i} + 4 \hat {j} - 2 \hat {k} .⟹
BC
=(3x−5)
i
^
+4
j
^
−2
k
^
.
\sf \implies as \ we\ know \ that = \vec {r} = \vec {a} + \lambda \vec {b} .⟹as we know that=
r
=
a
+λ
b
.
\sf \implies 2 \hat {i} - (1 - y) \hat {j} - 2 \hat {k} =\lambda [(3x - 5) \hat{i} + 4 \hat {j} - 2 \hat {k} ] .⟹2
i
^
−(1−y)
j
^
−2
k
^
=λ[(3x−5)
i
^
+4
j
^
−2
k
^
].
\sf \implies 2 = \lambda(3x - 5). =(1).⟹2=λ(3x−5).=(1).
\sf \implies -(1 - y) = 4 \lambda =(2).⟹−(1−y)=4λ=(2).
\sf \implies -2 = -2 \lambda = (3)⟹−2=−2λ=(3)
From equation, (3) we get.
⇒ 2 = 2λ.
⇒ λ = 1.
Put the value of λ in equation, (1) and (2) we get.
⇒ 2 = 1(3x - 5).
⇒ 2 = 3x - 5.
⇒ 8 = 3x.
⇒ x = 8/3.
⇒ -(1 - y) = 4.
⇒ - 1 + y = 4.
⇒ y = 5.
Value of x = 8/3 y = 5 λ = 1
As the point divides in the ratio of k or 1, we get,
Co-ordinates are,
A = (3,-1,2).
B = (5,-1,1).
C = (8,3,-1).
\sf \implies \vec {OA} = 3 \hat {i} - y \hat {j} + 2\hat {k}⟹
OA
=3
i
^
−y
j
^
+2
k
^
\sf \implies \vec {OB} = 5 \hat {i} - \hat {j} +\hat {k}⟹
OB
=5
i
^
−
j
^
+
k
^
\sf \implies \vec {OC} = 3x \hat {i} + 3 \hat {j} - \hat {k}⟹
OC
=3x
i
^
+3
j
^
−
k
^
\sf \implies \vec {OB} = \dfrac{k \vec {(OC)} + 1\vec {(OA) }}{k + 1}⟹
OB
=
k+1
k
(OC)
+1
(OA)
\sf \implies 5 \hat {i} - \hat {j} + \hat {k} = \dfrac{k[8 \hat {i} + 3 \hat {j} - \hat {k] + 1[3 \hat {i} - 5 \hat {j} + 2 \hat {k]}}}{k + 1}⟹5
i
^
−
j
^
+
k
^
=
k+1
k[8
i
^
+3
j
^
−
k]+1[3
i
^
−5
j
^
+2
k]
^
^
\sf \implies 5 \hat {i} - \hat {j} + \hat {k} = \dfrac{(8k + 3) \hat {i} + (3k - 5) \hat {j} - (k - 2)\hat {k}}{k + 1}⟹5
i
^
−
j
^
+
k
^
=
k+1
(8k+3)
i
^
+(3k−5)
j
^
−(k−2)
k
^
\sf \implies 5 \hat {i} - \hat {j} + \hat {k} = \dfrac{(8k + 3) \hat {i}}{k + 1} = \dfrac{(3k - 5 ) \hat {j}}{k + 1} = \dfrac{-(k - 2) \hat {k}}{k + 1}⟹5
i
^
−
j
^
+
k
^
=
k+1
(8k+3)
i
^
=
k+1
(3k−5)
j
^
=
k+1
−(k−2)
k
^
\sf \implies \dfrac{8k + 3}{k + 1} = 5⟹
k+1
8k+3
=5
⇒ 8k + 3 = 5 ( k + 1 ).
⇒ 8k + 3 = 5k + 5.
⇒ 8k - 5k = 5 - 3.
⇒ 3k = 2.
⇒ k = 2/3.
⇒ 3k - 5/k + 1 = -1.
⇒ 3k - 5 = - 1(k + 1).
⇒ 3k - 5 = -k - 1.
⇒ 3k + k = -1 + 5.
⇒ 4k = 4.
⇒ k = 1.
⇒ -(k - 2)/k + 1 = 1.
⇒ -k + 2 = k + 1.
⇒ 0.
Thus, B divides AC into ratio = 2/3 or 1