Show that the vectors 2 -3 -4 k- and -4 -6 -8 k- are collinear-

Let a=2î 3ĵ+4k̂ and b= 4î+6ĵ 8k̂ It is observed that b= 4î+6ĵ 8k̂= 2(2î 3ĵ+4k̂)= 2a ∴ b=λ a, where λ = 2 Vectors a and b have the same direction, ther ...

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Standard XII

Physics

Acceleration in 2D

Show that the...

Question

Show that the vectors $2^i - 3^j + 4^k a n d - 4^i + 6^j - 8^k$ are collinear.

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Solution

Let $a = 2^i - 3^j + 4^k a n d b = - 4^i + 6^j - 8^k$
It is observed that $b = - 4^i + 6^j - 8^k = - 2 (2^i - 3^j + 4^k) = - 2 a$
$∴ b = λ a, w h e r e λ = - 2$
Vectors a and b have the same direction, therefore they are collinear.

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Q. Show that the vectors

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2^i - 3^j + 4^k a n d - 4^i + 6^j - 8^k

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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 It is observed that b=−4^i+6^j−8^k=−2(2^i−3^j+4^k)=−2a ∴ b=λa, where λ =−2 Vectors a and b have the same direction, therefore they are collinear.

Show that the vectors $2^i - 3^j + 4^k a n d - 4^i + 6^j - 8^k$ are collinear.

Let $a = 2^i - 3^j + 4^k a n d b = - 4^i + 6^j - 8^k$
It is observed that $b = - 4^i + 6^j - 8^k = - 2 (2^i - 3^j + 4^k) = - 2 a$
$∴ b = λ a, w h e r e λ = - 2$
Vectors a and b have the same direction, therefore they are collinear.