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

$\to V = 2^i +^j -^k$ and $\to W =^i + 3^k$ . If $\to U$ is a unit vector, then the maximum value of the scalar triple product $[\to U \to V \to W]$ is

Q. Let

\to u = \to i + \to j, \to v = \to i - \to j

and

\to ω = \to i + 2 \to j + 3 \to k .

^n

unit vector such that

\to u \cdot^n = 0

and

\to v \cdot^n = 0

then

| \to w \cdot^n |

is equal to

Join BYJU'S Learning Program

Let →u=^i+^j,→v=^i−^j and →w=^i+2^j+3^k. 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 D 3Let ^n=x^i+y^j+z^k, where x2+y2+z2=1.Now, →u.^n=0(^i+^j).(x^i+y^j+z^k)=0x+y=0−−−(1)Also, →v.^n=0(^i−^j).(x^i+y^j+z^k)=0x−y=0−−−(2)Solving (1) and (2), we get x=y=0. Thus z=1or−1 (because x2+y2+z2=1Thus, →w.^n=(^i+2^j+3^k).(±^k)=±3

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