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Vector Algebra

Section: Mathematics
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Question : 2 of 38
 
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Consider the vectors
→
x
=
∧
i
+2
∧
j
+3
∧
k
,‌‌
→
y
=2
∧
i
+3
∧
j
+
∧
k
‌ and ‌
→
z
=3
∧
i
+
∧
j
+2
∧
k
For two distinct positive real numbers α and β, define
→
X
=α
→
x
+β
→
y
−
→
z
,
→
Y
=α
→
y
+β
→
z
−
→
x
,‌ and ‌
→
Z
=α
→
z
+β
→
x
−
→
y
.
If the vectors
→
X
,
→
Y
, and
→
Z
 lie in a plane, then the value of α+β−3 is ____
[JEE Adv 2025 P2]
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