Let a- b- and c- be three units vectors such that 3a- - 4b- - 5c- - 0- then which of the following statements is true-

The correct option is D None of theseGiven, 3a⃗+4b⃗+5c⃗=0 They are coplanar a⃗= 53c⃗ 43b⃗ a⃗.b⃗= 53c⃗.b⃗ 43b⃗.b⃗= 53c⃗.b⃗ 43 Since a⃗.b⃗ ca ...

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Byju's Answer

Standard XII

Mathematics

Condition for Coplanarity of Four Points

Let a⃗, b⃗ ...

Question

Let $\to a, \to b$ and $\to c$ be three units vectors such that $3 \to a + 4 \to b + 5 \to c = 0$ , then which of the following statements is true?

\to a

is parallel to

\to b

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\to a

is perpendicular to

\to b

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\to a

is neither parallel nor perpendicular to

\to b

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None of these

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Solution

The correct option is D None of these
Given, $3 \to a + 4 \to b + 5 \to c = 0$
They are coplanar
$\to a = - \frac{5}{3} \to c - \frac{4}{3} \to b$
$\to a . \to b = - \frac{5}{3} \to c . \to b - \frac{4}{3} \to b . \to b = - \frac{5}{3} \to c . \to b - \frac{4}{3}$
Since $\to a . \to b$ cant be equal to 1 So $\to a$ cant be parellel to $\to b$
$\to a . \to b$ can be equal to zero but not strictly
So, $\to a$ cant be strictly perpendicular to $\to b$
So, answer is option D.

Suggest Corrections

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Let →a,→b and →c be three units vectors such that 3→a+4→b+5→c=0, then which of the following statements is true?

Let $\to a, \to b$ and $\to c$ be three units vectors such that $3 \to a + 4 \to b + 5 \to c = 0$ , then which of the following statements is true?