Given the vectors u-2-k- v-2k- w-k-If the volume of the parallelepiped having -c u- v- and c w- as concurrent edges- is 8 then -c- can be equal to

The correct option is A ± 2 Volume of a parallelepiped having sides a⃗ , b⃗ and c⃗ is a⃗· (b⃗×c⃗) Volume =[ cu⃗ v⃗ cw⃗ #1 ...

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

Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Given the vec...

Question

Given the vectors
$\to u = 2^i -^j -^k$
$\to v =^i -^j + 2^k$
$\to w =^i -^k$
If the volume of the parallelepiped having $- c \to u, \to v$ and $c \to w$ as concurrent edges, is $8$ then $^{'} c^{'}$ can be equal to

\pm 2

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

4

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

8

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

can not be determined

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

Open in App

Solution

The correct option is A $\pm 2$
Volume of a parallelepiped having sides $\to a$ , $\to b$ and $\to c$ is
$\to a \cdot (\to b \times \to c)$
Volume $= [- c \to u \to v c \to w]$
$= ∣ ∣ ∣ ∣ \begin{matrix} - 2 c & c & c 1 & - 1 & 2 c & 0 & - c \end{matrix} ∣ ∣ ∣ ∣$
$= (- 2 c) (c) + c (2 c - c) + c (- (- c)) = 8 o r 2 c^{2} = 8 o r c = \pm 2$

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. Find a vector

\to v

which is co-planar with the vectors

\to a =^i - 2^j +^k

and

\to b =^i -^j + 2^k

and is orthogonal to the vector

\to c = - 2^i +^j +^k

. It is given that the projection of

\to v

along the vector

^i -^j +^k

is equal to

16 \sqrt{3}

Find the volume of the parallelepiped whose coterminous edges are represented by vectors

\to a =^i +^j +^k; \to b = 2^i + 4^j -^k

and

\to c =^i +^j + 3^k

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. If the vectors

2^i - 3^j,^i +^j -^k

and

3^i -^k

form three concurrent edges of a parallelopiped, then the volume of the parallelopiped is

Join BYJU'S Learning Program

Given the vectors→u=2^i−^j−^k→v=^i−^j+2^k→w=^i−^kIf the volume of the parallelepiped having −c→u,→v and c→w as concurrent edges, is 8 then ′c′ can be equal to

The correct option is A ±2Volume of a parallelepiped having sides →a, →b and →c is →a⋅(→b×→c)Volume =[−c→u→vc→w] =∣∣ ∣∣−2ccc1−12c0−c∣∣ ∣∣ =(−2c)(c)+c(2c−c)+c(−(−c))=8or2c2=8orc=±2

Given the vectors
$\to u = 2^i -^j -^k$
$\to v =^i -^j + 2^k$
$\to w =^i -^k$
If the volume of the parallelepiped having $- c \to u, \to v$ and $c \to w$ as concurrent edges, is $8$ then $^{'} c^{'}$ can be equal to