Show that the vector is parallel to a vector A-2k- is parallel to a vector B-3-3-6k-

The correct option is A 1/3 times the magnitude of B⃗. A vector A⃗ is parallel to an another vector B⃗ if it can be written as A⃗= m ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Show that the...

Question

Show that the vector is parallel to a vector $\to A =^i -^j + 2^k$ is parallel to a vector $\to B = 3^i - 3^j + 6^k .$

\frac{1}{3}

times the magnitude of

\to B .

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\frac{1}{4}

times the magnitude of

\to B .

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\frac{1}{2}

times the magnitude of

\to B .

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None of these

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Solution

The correct option is A $\frac{1}{3}$ times the magnitude of $\to B .$
A vector $\to A$ is parallel to an another vector $\to B$ if it can be written as
$\to A = m \to B$ where $m$ is a constant.
Here, $\to A = (^i -^j + 2^k) = \frac{1}{3} (3^i - 3^j + 6^k)$
or $\to A = \frac{1}{3} \to B$
This implies that $\to A | | \to B$ and magnitude of $\to A$ is $\frac{1}{3}$ times the magnitude of $\to B .$

Suggest Corrections

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12

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Show that the vector is parallel to a vector →A=^i−^j+2^k is parallel to a vector →B=3^i−3^j+6^k.

Show that the vector is parallel to a vector $\to A =^i -^j + 2^k$ is parallel to a vector $\to B = 3^i - 3^j + 6^k .$