Let -k-b-2k- and -x-x-2-k- If the vector - lies in the plane of - and b- then x equals

Since the three vectors are coplanar 1 amp; 1 amp; 1 1 amp; 1 amp; 2 x amp; x 2 amp; 1 =0 ⇒ 1 amp; 0 amp; 0 1 amp; 2 amp; 1 ...

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Byju's Answer

Standard XI

Mathematics

Test for Coplanarity

Let â=î+ĵ+k̂,...

Question

Let $^a =^i +^j +^k,^b =^i -^j + 2^k$ and $^c = x^i + (x - 2)^j -^k$ . If the vector $^c$ lies in the plane of $^a$ and $^b$ , then x equals

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Solution

The correct option is D -2
Since the three vectors are coplanar $∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & - 1 & 2 x & x - 2 & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & 0 1 & - 2 & 1 x & - 2 & - 1 - x \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow - 2 (- 1 - x) + 2 = 0 \Rightarrow x = - 2$

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Let ^a=^i+^j+^k,^b=^i−^j+2^k and ^c=x^i+(x−2)^j−^k. If the vector ^c lies in the plane of ^a and ^b, then x equals

The correct option is D -2Since the three vectors are coplanar ∣∣ ∣∣1111−12xx−2−1∣∣ ∣∣=0⇒∣∣ ∣∣1001−21x−2−1−x∣∣ ∣∣=0⇒−2(−1−x)+2=0⇒x=−2

Let $^a =^i +^j +^k,^b =^i -^j + 2^k$ and $^c = x^i + (x - 2)^j -^k$ . If the vector $^c$ lies in the plane of $^a$ and $^b$ , then x equals