Question

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If Alpha X A B Y B C Zc A And A B C 18 Then X Y Z Is Equal To?
✳️need proper answer
✳️gud luck :-P​

Answer 1

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If Alpha X A B Y B C Zc A And A B C 18 Then X Y Z =α. (a + b + c)

α = x (a × b) + y (b × c) + z(c × a)

α.a = x (a × b).a + y (b × c).a + z(c × a).a

α.a = 0+y(b × c).a +0

α.a = y [abc]

Also, given,

[abc] = ⅛

So, y = α.a/[abc] = 8 α.a

Similarly,

α.b = z(c × a).b = z[abc]

So, z = 8 α b

Again,

α.c = x(a x b).c = x[abc]

So, x = 8αc

Hence,

x+y+z = 8αc+8αa+8αb

= 8α (a+b+c)

Answer 2

Answer:

1) 8 α. (a + b + c)

2) α . (a + b + c)

3) 8(a + b + c)

4) None of these

Answer:(1) 8 α. (a + b + c)

Solution: α = x (a × b) + y (b × c) + z(c × a)

α.a = x (a × b).a + y (b × c).a + z(c × a).a

α.a = 0+y(b × c).a +0

α.a = y [abc]

Also, given,

[abc] = ⅛

So, y = α.a/[abc] = 8 α.a

Similarly,

α.b = z(c × a).b = z[abc]

So, z = 8 α b

Again,

α.c = x(a x b).c = x[abc]

So, x = 8αc

Hence,

x+y+z = 8αc+8αa+8αb

= 8α (a+b+c)