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Question

Assertion :If a^i+^j+^k,^i+b^j+^k,^i+^j+c^k are coplanar, then 11a+11b+11c=1 provided a1,b1,c1. Reason: Vectors a,b,c are coplanar, then a(b×c)=0.

A
Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
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B
Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
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C
Assertion is true but Reason is false
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D
Assertion is false but Reason is true
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Solution

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
Three vectors ¯a,¯b,¯c are coplanar then
[¯a¯b¯c]=¯a(¯bׯc)
Reason is true & Correct explanation for Assertion (A)
Now , a^i+^j+^k,^i+b^j+^k,^i+^j+c^k are given coplanar
∣ ∣a111b111c∣ ∣[^i^j^k]=0
∣ ∣a111b111c∣ ∣=0 as ^i(^j×^k)=1
Using C2C2C1,C3C3C2
∣ ∣a1a01b11b10c1∣ ∣=0
a(b1)(c1)(1a)[(c1)(1b)]=0
a(b1)(c1)(1a)(c1)+(1a)(1b)=0
on dividing by (1a)(1b)(1c)=0
1(1a)1a+11b+11c=0
11a+11b+11c=1
Assertion (A) is true .

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