If direction cosines of a vector of magnitude 3 are 2-3- -1-3- 2-3 and a -0- then vector isA- 2 -2 k-B- 2 -2 k-C- -2 -2 k-D- -2 -2 k-

Vector whose D.C.'s are nbsp;23, 13, 23 and magnitude 3 is 3×(23nbsp; i+ 13ĵ+23k̂) =2î ĵ+2k̂ ...

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Standard XII

Mathematics

Direction Cosines

If direction ...

Question

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

2^i +^j + 2^k

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2^i -^j + 2^k

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^i - 2^j + 2^k

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^i + 2^j + 2^k

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Solution

The correct option is B $2^i -^j + 2^k$
Vector whose D.C.'s are $\frac{2}{3}, \frac{- 1}{3}, \frac{2}{3}$ and magnitude $3$ is $3 \times (\frac{2}{3}^i + \frac{- 1}{3}^j + \frac{2}{3}^k)$
$= 2^i -^j + 2^k$

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If direction cosines of a vector of magnitude 3 are 23, −13, 23 and a>0, then vector is

The correct option is B 2^i−^j+2^kVector whose D.C.'s are 23, −13, 23 and magnitude 3 is 3×(23^i+−13^j+23^k) =2^i−^j+2^k

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 correct option is B $2^i -^j + 2^k$
Vector whose D.C.'s are $\frac{2}{3}, \frac{- 1}{3}, \frac{2}{3}$ and magnitude $3$ is $3 \times (\frac{2}{3}^i + \frac{- 1}{3}^j + \frac{2}{3}^k)$
$= 2^i -^j + 2^k$