Show that the vectors 2 i - 3 j + 4 k and - 4 i + 6 j - 8 k are collinear.

Let a = 2 i - 3 j + 4 k and b = - 4 i + 6 j - 8 k Now, b = - 2(2 i - 3 j + 4 k) = - 2 a b is a scalar multiple of a a and b have same direction. Hence, a and b are collinear.

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 440,Ex.10.2,Q.No 11

Question

Show that the vectors $2\hat i - 3\hat j + 4\hat k$ and $- 4\hat i + 6\hat j - 8\hat k$ are collinear.

Step-by-step Solution

Let $\vec a = 2\hat i - 3\hat j + 4\hat k$ and $\vec b = - 4\hat i + 6\hat j - 8\hat k$
Now, $\vec b = - 2(2\hat i - 3\hat j + 4\hat k) = - 2\vec a$

$\Rightarrow \vec b$ is a scalar multiple of $\vec a \Rightarrow \vec a$ and $\vec b$ have same direction.
Hence, $\vec a$ and $\vec b$ are collinear.

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