A - b and c are three nonzero- non collinear vectors- If the vector 3 a -7 b is collinear with c and 3 b -2 c is collinear with a- then Let -9 a-21 b-14 c- is equal to

3 a⃗+7 b⃗ is collinear with c⃗ ⇒ 3 a⃗+7 b⃗=λc⃗ ... (1) 3 b⃗+2c⃗ is collinear with a⃗ ⇒ 3 b⃗+2c⃗=μa⃗ ... (2) Finding out b⃗ from (1) and putting it in (2), we ...

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Byju's Answer

Standard XII

Mathematics

Fundamental Theorem In 3D

a , b and c a...

Question

Let $\to a, \to b$ and $\to c$ are three nonzero, non collinear vectors. If the vector $3 \to a + 7 \to b$ is collinear with $\to c$ and $3 \to b + 2 \to c$ is collinear with $\to a$ , then $∣ ∣ 9 \to a + 21 \to b + 14 \to c ∣ ∣$ is equal to

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Solution

$3 \to a + 7 \to b$ is collinear with $\to c$
$\Rightarrow 3 \to a + 7 \to b = λ \to c$ ... (1)

$3 \to b + 2 \to c$ is collinear with $\to a$
$\Rightarrow 3 \to b + 2 \to c = μ \to a$ ... (2)

Finding out $\to b$ from (1) and putting it in (2), we get,
$3 \times \frac{λ \to c - 3 \to a}{7} + 2 \to c = μ \to a$
$\Rightarrow 3 λ \to c - 9 \to a + 14 \to c = 7 μ \to a$
$\Rightarrow \to c (3 λ + 14) = \to a (7 μ + 9)$

Since, $\to a$ and $\to c$ are not collinear,
$3 λ + 14 = 0 \Rightarrow λ = - \frac{14}{3}$ and
$7 μ + 9 = 0 \Rightarrow μ = - \frac{9}{7}$

Putting the value of $μ$ in (2), we get,
$3 \to b + 2 \to c = - \frac{9 \to a}{7}$
$\Rightarrow 9 \to a + 21 \to b + 14 \to c = 0$

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Let →a, →b and →c are three nonzero, non collinear vectors. If the vector 3 →a+7 →b is collinear with →c and 3 →b+2→c is collinear with →a, then ∣∣9 →a+21 →b+14 →c∣∣ is equal to

Let $\to a, \to b$ and $\to c$ are three nonzero, non collinear vectors. If the vector $3 \to a + 7 \to b$ is collinear with $\to c$ and $3 \to b + 2 \to c$ is collinear with $\to a$ , then $∣ ∣ 9 \to a + 21 \to b + 14 \to c ∣ ∣$ is equal to