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Question : 67 of 120
Marks:
+1,
-0
Solution:
Given,
The vector
=(×)×Statement
I: is coplanar with
and
.
We use the vector triple product identity:
(×)×=(⋅)−(⋅).
This shows that
is a linear combination of
and
, hence
is coplanar with
and
.
Therefore, Statement I is correct.
Statement II:
is perpendicular to
.
To check this, compute the dot product
â‹…. Using the vector triple product identity, we find:
⋅=(⋅)(⋅)−(⋅)(⋅)=0which means
is perpendicular to
.
Therefore, Statement II is correct.
∴ Both Statement I and Statement II are correct.
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