Let A(t)=f1(t)i^+f2(t)j^andB(t)=g(t)i^+g2(t)j^,t∈[0,1],f1,f2,g1g2 are continuous functions. If A(t)andB(t) are non-zero vectors for all tandA(0)=2i^+3j^,A(1)=6i^+2j^,B(0)=3i^+2i^andB(1)=2j^+6j^ Then,show that A(t)andB(t) are parallel for some t.

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Question

Let $A (t) = f_{1} (t) \hat{i} + f_{2} (t) \hat{j} and B (t) = g (t) \hat{i} + g_{2} (t) \hat{j}, t \in [0, 1], f_{1}, f_{2}, g_{1} g_{2}$ are continuous functions. If $A (t) and B (t)$ are non-zero vectors for all $t and A (0) = 2 \hat{i} + 3 \hat{j}, A (1) = 6 \hat{i} + 2 \hat{j}, B (0) = 3 \hat{i} + 2 \hat{i} and B (1) = 2 \hat{j} + 6 \hat{j}$ Then,show that $A (t) and B (t)$ are parallel for some $t$ .

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Noah Discussed

Let

A (t) = f_{1} (t) \hat{i} + f_{2} (t) \hat{j} and B (t) = g (t) \hat{i} + g_{2} (t) \hat{j}, t \in [0, 1], f_{1}, f_{2}, g_{1} g_{2}

are continuous functions. If

A (t) and B (t)

are non-zero vectors for all

t and A (0) = 2 \hat{i} + 3 \hat{j}, A (1) = 6 \hat{i} + 2 \hat{j}, B (0) = 3 \hat{i} + 2 \hat{i} and B (1) = 2 \hat{j} + 6 \hat{j}

Then,show that

A (t) and B (t)

are parallel for some

t

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Question Text

Let

A (t) = f_{1} (t) \hat{i} + f_{2} (t) \hat{j} and B (t) = g (t) \hat{i} + g_{2} (t) \hat{j}, t \in [0, 1], f_{1}, f_{2}, g_{1} g_{2}

are continuous functions. If

A (t) and B (t)

are non-zero vectors for all

t and A (0) = 2 \hat{i} + 3 \hat{j}, A (1) = 6 \hat{i} + 2 \hat{j}, B (0) = 3 \hat{i} + 2 \hat{i} and B (1) = 2 \hat{j} + 6 \hat{j}

Then,show that

A (t) and B (t)

are parallel for some

t