If a and b are proper vectors and a - b - 0- then

The correct option is B a and b are collinear a⃗×b⃗=0⃗ a>b>sinθ>n̂=0⃗ as >given> a, b ≠ 0 ∴>sinθ=0 it >means >θ=0^0 ...

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Standard XII

Mathematics

Test for Collinearity of Vectors

If a and ...

Question

If $a$ and $b$ are proper vectors and $a \times b = 0$ , then

a and b are collinear

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a and b are dependent

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a and b are orthogonal

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none of these

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Solution

The correct option is B a and b are collinear

$\to a \times \to b = \to 0 a b s i n θ^n = \to 0 a s g i v e n a, b \neq 0 ∴ s i n θ = 0 i t m e a n s θ = 0^{0}$
hence vectors are collinear.

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If a and b are proper vectors and a×b=0, then

The correct option is B a and b are collinear→a×→b=→0absinθ^n=→0asgivena,b≠0∴sinθ=0itmeansθ=00hence vectors are collinear.

If $a$ and $b$ are proper vectors and $a \times b = 0$ , then

The correct option is B a and b are collinear

$\to a \times \to b = \to 0 a b s i n θ^n = \to 0 a s g i v e n a, b \neq 0 ∴ s i n θ = 0 i t m e a n s θ = 0^{0}$
hence vectors are collinear.