Let u-i-j- v-i-j and w-i-2j-3k- If n- is a unit vector such that u-n-0 and v-n-0- then -w-n- is equal to

The correct option is A 3 We have, u. n̂=0 and v. n̂=0 ⇒n̂⊥ u and n̂⊥ v ∴n̂=±u× v|u× v| Now, u × v=(i+j)× (i j)=2k ∴n ...

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Standard XII

Mathematics

Applications of Dot Product

Let u=i+j, ...

Question

Let $u = i + j, v = i - j$ and $w = i + 2 j + 3 k$ . If $^n$ is a unit vector such that $u \cdot^n = 0$ and $v \cdot^n = 0$ , then $| w \cdot^n |$ is equal to

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Solution

The correct option is A $3$
We have, $u .^n = 0$ and $v .^n = 0$
$\Rightarrow^n ⊥ u$ and $^n ⊥ v$

$∴^n = \pm \frac{u \times v}{| u \times v |}$

Now, $u \times v = (i + j) \times (i - j) = 2 k$
$∴^n = \pm k$
Hence, $| ¯ w \cdot^n | = | (i + 2 j + 3 k) \cdot (\pm k) | = 3$

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Let u=i+j,v=i−j and w=i+2j+3k. If ^n is a unit vector such that u⋅^n=0 and v⋅^n=0, then |w⋅^n| is equal to

The correct option is A 3We have, u.^n=0 and v.^n=0⇒^n⊥u and ^n⊥v∴^n=±u×v|u×v|Now, u×v=(i+j)×(i−j)=2k∴^n=±kHence, |¯w⋅^n|=|(i+2j+3k)⋅(±k)|=3

Let $u = i + j, v = i - j$ and $w = i + 2 j + 3 k$ . If $^n$ is a unit vector such that $u \cdot^n = 0$ and $v \cdot^n = 0$ , then $| w \cdot^n |$ is equal to

The correct option is A $3$
We have, $u .^n = 0$ and $v .^n = 0$
$\Rightarrow^n ⊥ u$ and $^n ⊥ v$

$∴^n = \pm \frac{u \times v}{| u \times v |}$

Now, $u \times v = (i + j) \times (i - j) = 2 k$
$∴^n = \pm k$
Hence, $| ¯ w \cdot^n | = | (i + 2 j + 3 k) \cdot (\pm k) | = 3$