Velocity of a particle is v -6 -2 -2 k- The component of the velocity parallel to vector a -k- in vector form isA- 6 -2 -2 k-B- -k-C- 2 -2 -2 k-D- 6 -2 -2 k-

The correct option is C 2î+ 2ĵ+2k̂Given, a vector v⃗ nbsp; and a unit vector n̂, you can divide the vector nbsp;v⃗ nbsp;into two parts nbsp;v⃗=p⃗+q⃗ wh ...

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Standard XII

Physics

Magnitude of Instantaneous Velocity

Velocity of a...

Question

Velocity of a particle is $\to v = 6^i + 2^j - 2^k$ . The component of the velocity parallel to vector $a =^i +^j -^k$ in vector form is

6^i + 2^j + 2^k

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2^i + 2^j + 2^k

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^i +^j +^k

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6^i + 2^j - 2^k

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Solution

The correct option is B $2^i + 2^j + 2^k$
Given, a vector $\to v$ and a unit vector $^n$ , you can divide the vector $\to v$ into two parts $\to v = \to p + \to q$
where $\to p$ and $\to q$ are parallel and perpendicular to $^n$ respectively. Now, the magnitude of $\to p$ is given by $\to p .^n$ .
Since $\to q .^n = 0$ , we have,
$| \to p | = \to p .^n = \to v .^n$
thus,
$\to p = | \to p |^n = (\to v .^n)^n$
Since the unit vector in the direction of $\to a$ is given by $\frac{\to a}{| \to a |}$ , the component of $\to v$ parallel to $\to a$ is given by
$(\to v . \frac{\to a}{| \to a |}) \frac{\to a}{| \to a |} = \frac{(\to v . \to a) \to a}{| \to a |^{2}}$
So, for the given problem, the component that we get is
$\frac{(6^i + 2^j - 2^k) (^i +^j +^k)}{(^i +^j +^k) (^i +^j +^k)} (^i +^j +^k) = 2^i + 2^j + 2^k$

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Similar questions

Q. The velocity of a particle is

\to v = 6^i + 2^j - 2^k .

The component of the velocity parallel to vector

\to a =^i +^j +^k

is :-

Q. If direction cosines of a vector of magnitude

3

are

\frac{2}{3}, \frac{- 1}{3}, \frac{2}{3}

and

a > 0

, then vector is

The vector in the direction of the vector $^i - 2^j + 2^k$ that has magnitude 9 is

(a) $^i - 2^j + 2^k$

(b) $\frac{^i - 2^j + 2^k}{3}$

(d) $9 (^i - 2^j + 2^k)$

_{1} =^i +^j + 2^k + λ (3^i - 2^j + 4^k)

_{2} = 2^i +^j + 3^k + μ (- 6^i + 4^j - 8^k)

The given vectors can form sides of a triangle $^i -^j -^k, - 2^i + 3^j -^k,^i - 2^j + 2^k$

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Velocity of a particle is →v=6^i+2^j−2^k. The component of the velocity parallel to vector a=^i+^j−^k in vector form is

Velocity of a particle is $\to v = 6^i + 2^j - 2^k$ . The component of the velocity parallel to vector $a =^i +^j -^k$ in vector form is