Between the following two statements: Statement-I: Let a = i + 2 j - 3 k and b = 2 i + j - k. Then the vector r satisfying a r = a b and a r = 0 is of magnitude 10. Statement-II: In a triangle ABC,…

Between the following two statements: Statement-I: Let a = i + 2… — Solution | JEE Mathematics

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Between the following two statements:

Statement-I: Let $\vec{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ . Then the vector $\vec{r}$ satisfying $\vec{a} \times \vec{r} = \vec{a} \times \vec{b}$ and $\vec{a} \cdot \vec{r} = 0$ is of magnitude $\sqrt{10}$ .

Statement-II: In a triangle $ABC$ , $\cos(2A) + \cos(2B) + \cos(2C) \geq -\frac{3}{2}$ .

A
Both Statement-I and Statement-II are incorrect
B
Statement-I is incorrect but Statement-II is correct
C
Both Statement-I and Statement-II are correct
D
Statement-I is correct but Statement-II is incorrect

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: Two statements are to be checked. The solution explicitly states, "The Correct Option is D".

Find: The correct option among the given statements.

The solution does not contain the intermediate working. It only gives the final conclusion that the correct option is D.

Therefore, based on the solution, Statement-I is correct but Statement-II is incorrect.

Common mistakes

Using the answer key instead of the solution. Here the page solution explicitly marks D as correct, so the solution must be treated.
Assuming both statements must be checked independently from scratch even when the solution already gives the final option. In extraction, the final marked option on the solution is authoritative.

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Answer

Step-by-step solution

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