CBSE Class 12 Sample Paper for 2022 Boards (For Term 2)

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## If š ā ā  0 ā, š ā. š ā = š ā. š ā, š ā Ć š ā = š ā Ć š ā , then show that š ā = š ā.

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Question 9 If š ā ā  0 ā, š ā. š ā = š ā. š ā, š ā Ć š ā = š ā Ć š ā , then show that š ā = š ā. Given that š ā. š ā = š ā. š ā Now, š ā. š ā = š ā. š ā š ā. š ā ā š ā. š ā = 0 š ā. (š ā ā š ā) = 0 Thus, either (š ā ā š ā) = š ā Or š ā is perpendicular to (š ā ā š ā) š ā Ć š ā = š ā Ć š ā Now, š ā Ć š ā = š ā Ć š ā š ā Ć š ā ā š ā Ć š ā = š ā š ā Ć (š ā ā š ā) = š ā Thus, either (š ā ā š ā) = š ā Or š ā is parallel to (š ā ā š ā) Since š ā cannot both be perpendicular and parallel to (š ā ā š ā) Therefore, the only other solution is (š ā ā š ā) = 0 ā š ā = š ā Hence proved