If a- -k-b- x-1-xk- and c- y-x-1-x-yk- then -a-b-c- - depends on

The correct option is D Neither on x nor on y [ a̅b̅c̅ ] = | 1 amp;0 #160; amp; 1 x #160; amp;1 #160; amp;1 x ...

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

Byju's Answer

Standard XII

Mathematics

Global Maxima

If a̅= î-k̂...

Question

If $¯ a =^i -^k, ¯ b = x^i +^j + (1 - x)^k$ and $¯ c = y^i + x^j + (1 + x - y)^k$ , then $[¯ a ¯ b ¯ c]$ depends on

Only

y

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

Only

x

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

On both

x

and

y

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

Neither on

x

nor on

y

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

Open in App

Solution

The correct option is D Neither on $x$ nor on $y$
$[¯ a ¯ b ¯ c]$

$= ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & - 1 x & 1 & 1 - x y & x & (1 + x - y) \end{matrix} ∣ ∣ ∣ ∣$

$= (1 + x - y - x + x^{2}) - (x^{2} - y)$

$= 1 - y + x^{2} - x^{2} + y$

$= 1$

Suggest Corrections

Similar questions

Q. Let

\to a =^i -^k, \to b = x^i +^j + (1 - x)^k

and

\to c = y^i + x^j + (1 + x - y)^k,

then

[\to a \to b \to c]

depends on

Q. Let

\to a =^i -^k

\to b = x^i +^j + (1 - x)^k

and

\to c = y^i + x^j + (1 + x - y)^k

, then

[\to a, \to b, \to c]

depends on

Q. Let

¯ a =^i +^j +^k, ¯ b =^i -^j + 2^k

and

¯ c = x^i + (x - 2)^j -^k .

If the vectors

\to c

lies in the plane of

¯ a

and

¯ b

, then

x

equals

Q. Let

^i,^j,^k

be three mutually or orthogonal unit vectors and let

x, y, z

be three distinct real numbers. If the vectors

\to u = x^i + y^j + z^k, \to v = y^i + z^j + x^k

and

\to w = z^i + x^j + y^k

are coplanar then

Q. If

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

and

\to c =^i + x^j + y^k

, are linearly dependent and

| \to c | = \sqrt{3}

then

(x, y)

Join BYJU'S Learning Program

If ¯a=^i−^k,¯b=x^i+^j+(1−x)^k and ¯c=y^i+x^j+(1+x−y)^k, then [¯a¯b¯c] depends on

The correct option is D Neither on x nor on y[¯a¯b¯c]=∣∣ ∣∣10−1x11−xyx(1+x−y)∣∣ ∣∣=(1+x−y−x+x2)−(x2−y)=1−y+x2−x2+y=1

If $¯ a =^i -^k, ¯ b = x^i +^j + (1 - x)^k$ and $¯ c = y^i + x^j + (1 + x - y)^k$ , then $[¯ a ¯ b ¯ c]$ depends on

The correct option is D Neither on $x$ nor on $y$
$[¯ a ¯ b ¯ c]$

$= ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & - 1 x & 1 & 1 - x y & x & (1 + x - y) \end{matrix} ∣ ∣ ∣ ∣$

$= (1 + x - y - x + x^{2}) - (x^{2} - y)$

$= 1 - y + x^{2} - x^{2} + y$

$= 1$