If π‘Žβƒ— β‰  0, βƒ—βƒ—βƒ— π‘Žβƒ—. 𝑏⃗⃗ = π‘Žβƒ—. 𝑐⃗, π‘Žβƒ— Γ— 𝑏⃗⃗ = π‘Žβƒ— Γ— 𝑐⃗, then show that 𝑏⃗⃗ = 𝑐⃗.

CBSE Sample Question Paper, Class 12 Mathematics Term 2 Question - If π‘Žβƒ— β‰  0, βƒ—βƒ—βƒ— π‘Žβƒ—. 𝑏⃗⃗ = π‘Žβƒ—. 𝑐⃗, π‘Žβƒ— Γ— 𝑏⃗⃗ = π‘Žβƒ— Γ— 𝑐⃗, then show that 𝑏⃗⃗ = 𝑐⃗.

By
Komal Kohli
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If π‘Žβƒ— β‰  0,
βƒ—βƒ—βƒ— π‘Žβƒ—. 𝑏⃗⃗ = π‘Žβƒ—. 𝑐⃗, π‘Žβƒ— Γ— 𝑏⃗⃗ = π‘Žβƒ— Γ— 𝑐⃗, then show that 𝑏⃗⃗ = 𝑐⃗.

Answer.

If π‘Žβƒ— β‰  0,
βƒ—βƒ—βƒ— π‘Žβƒ—. 𝑏⃗⃗ = π‘Žβƒ—. 𝑐⃗, π‘Žβƒ— Γ— 𝑏⃗⃗ = π‘Žβƒ— Γ— 𝑐⃗, then show that 𝑏⃗⃗ = 𝑐⃗.
Solution: We have π‘Žβƒ—. (𝑏⃗⃗ βˆ’ 𝑐⃗) = 0
β‡’ (𝑏⃗⃗ βˆ’ 𝑐⃗) = βƒ—0βƒ— or π‘Žβƒ— βŠ₯ (𝑏⃗⃗ βˆ’ 𝑐⃗)
β‡’ 𝑏⃗⃗ = 𝑐⃗ or π‘Žβƒ— βŠ₯ (𝑏⃗⃗ βˆ’ 𝑐⃗)
Also, π‘Žβƒ— Γ— (𝑏⃗⃗ βˆ’ 𝑐⃗) = βƒ—0βƒ—
β‡’ (𝑏⃗⃗ βˆ’ 𝑐⃗) = βƒ—0βƒ— or π‘Žβƒ— βˆ₯ (𝑏⃗⃗ βˆ’ 𝑐⃗)
β‡’ 𝑏⃗⃗ = 𝑐⃗ or π‘Žβƒ— βˆ₯ (𝑏⃗⃗ βˆ’ 𝑐⃗)
π‘Žβƒ— π‘π‘Žπ‘› π‘›π‘œπ‘‘ 𝑏𝑒 π‘π‘œπ‘‘β„Ž π‘π‘’π‘Ÿπ‘π‘’π‘›π‘‘π‘–π‘π‘’π‘™π‘Žπ‘Ÿ π‘‘π‘œ (𝑏⃗⃗ βˆ’ 𝑐⃗) π‘Žπ‘›π‘‘ π‘π‘Žπ‘Ÿπ‘Žπ‘™π‘™π‘’π‘™ π‘‘π‘œ (𝑏⃗⃗ βˆ’ 𝑐⃗)
Hence, 𝑏⃗⃗ = 𝑐⃗.

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