Let $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ be non coplanar vectors. The vectors $3 ¯ ¯ ¯ a - 2 ¯ ¯ b - 4 ¯ ¯ c$ , $- ¯ ¯ ¯ a + 2 ¯ ¯ c$ , $- 2 ¯ ¯ ¯ a + ¯ ¯ b + 3 ¯ ¯ c$ are

Linearly dependent

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Linearly independent

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Collinear

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Non collinear

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A Linearly dependent
Vectors are coplanar so we get
$3 \to a - 2 \to b - 4 \to c = λ (- \to a + 2 \to c) + μ (- 2 \to a + \to b + 3 \to c)$
Solving
$3 = - λ - 2 μ$ ------(1)
$μ = - 2, λ = 1$
So there Vectors are Linerly dependent

Suggest Corrections

Similar questions

\vec{a}

\vec{b}

\vec{c}

2 \vec{a} - \vec{b} + 3 \vec{c}, \vec{a} + \vec{b} - 2 \vec{c} and \vec{a} + \vec{b} - 3 \vec{c}

\vec{a} + 2 \vec{b} + 3 \vec{c}, 2 \vec{a} + \vec{b} + 3 \vec{c} and \vec{a} + \vec{b} + \vec{c}

2 \to a + 3 \to b - \to c, \to a - 2 \to b + 3 \to c, 3 \to a + 4 \to b - 2 \to c a n d \to a - 6 \to b + 6 \to c

\to a, \to b a n d \to c

Join BYJU'S Learning Program