Let V-2-k- W-3k- -U-2- If U- is a vector in x-y plane- then greatest value of -U-V-W-2-

The correct option is C 236 ([u⃗v⃗w⃗])^2=(u⃗(v⃗×w⃗))^2=(u⃗)^2 (v⃗×w⃗)^2 Given v⃗=2i+j k, w⃗=i+3k |v⃗|=2 i amp; j amp; k 2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Let V⃗=2î+ĵ...

Question

Let $\to V = 2^i +^j -^k, \to W =^i + 3^k, | \to U | = 2$ . If $\to U$ is a vector in x-y plane, then greatest value of $([\to U \to V \to W])^{2}$ .

232

No worries! We‘ve got your back. Try BYJU‘S free classes today!

340

No worries! We‘ve got your back. Try BYJU‘S free classes today!

236

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

312

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $236$
$([\to u \to v \to w])^{2} = (\to u (\to v \times \to w))^{2} = (\to u)^{2} (\to v \times \to w)^{2}$
Given $\to v = 2 i + j - k, \to w = i + 3 k$
$| \to v | = 2$
$∣ ∣ ∣ ∣ \begin{matrix} i & j & k 2 & 1 & - 1 1 & 0 & 3 \end{matrix} ∣ ∣ ∣ ∣ \begin{matrix} = i (3) - 1 (7) + k (- 1) = 3 i - 7 j - k \end{matrix}$
then we know
$(\to v, \to w) = | \to v \times \to w |^{2} = [\sqrt{(3)^{2} + (7)^{2} + (1)^{2}}]^{2}$
$= (\sqrt{59})^{2}$
$= 59$
So,
$([\to u \to v \to w])^{2} = | \to v |^{2} (\to v \times \to w)^{2}$
$= 4 \times 59$
$= 236$

Suggest Corrections

Similar questions

$\to V = 2^i +^j -^k$ 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. If

\to u =^j + 4^k

\to v =^i - 3^k

, and

\to w = cos θ^i + sin θ^j

are vectors in

3

-dimensional space, then the maximum possible value of

| \to u \times \to v \cdot \to w |

is?

Q. Let

\to u =^i +^j, \to v =^i -^j, \to w =^i + 2^j + 3^k

. If

\to n

is a unit vector such that

\to u \cdot \to n = 0, \to v \cdot \to n = 0

, then

| \to w \cdot \to n | =

Q. Let

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

and

\to w =^i + 2^j + 3^k

. If

^n

is a unit vector

\to u \cdot^n = 0

and

\to v \cdot^n = 0

, then

|^w \cdot^n |

is equal to?

Q. 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 .^n = 0

,then

| \to w .^n | =

Join BYJU'S Learning Program

Let →V=2^i+^j−^k,→W=^i+3^k,|→U|=2. If →U is a vector in x-y plane, then greatest value of ([→U→V→W])2.

Let $\to V = 2^i +^j -^k, \to W =^i + 3^k, | \to U | = 2$ . If $\to U$ is a vector in x-y plane, then greatest value of $([\to U \to V \to W])^{2}$ .