Let u-v-w-2-3k- If n- is a unit vector such that u-n- 0 and v-n- 0- then w-n- equals

The correct option is C 3 n̂ #160;will be in the direction of cross product of #160; u⃗ #160;and #160; v⃗ ∴n̂ = (î + #160;ĵ) ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let u̅=î+ĵ,...

Question

Let $¯ u =^i +^j, ¯ v =^i -^j, ¯ w =^i + 2^j + 3^k .$ If $^n$ is a unit vector such that $¯ u \cdot^n = 0$ and $¯ v \cdot^n = 0$ , then $| \begin{matrix} ¯ w \cdot^n \end{matrix} |$ equals

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Solution

The correct option is C $3$
$^n$ will be in the direction of cross product of $\to u$ and $\to v$

$∴^n = (^i +^j) \times (^i -^j) = - 2^k$
$\Rightarrow^n =^k$
Now $\to w .^n = (^i + 2^j + 3^k) .^k = 3$

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

The correct option is C 3^n will be in the direction of cross product of →u and →v∴^n=(^i+^j)×(^i−^j)=−2^k⇒^n=^kNow →w.^n=(^i+2^j+3^k).^k=3

Let $¯ u =^i +^j, ¯ v =^i -^j, ¯ w =^i + 2^j + 3^k .$ If $^n$ is a unit vector such that $¯ u \cdot^n = 0$ and $¯ v \cdot^n = 0$ , then $| \begin{matrix} ¯ w \cdot^n \end{matrix} |$ equals

The correct option is C $3$
$^n$ will be in the direction of cross product of $\to u$ and $\to v$

$∴^n = (^i +^j) \times (^i -^j) = - 2^k$
$\Rightarrow^n =^k$
Now $\to w .^n = (^i + 2^j + 3^k) .^k = 3$