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

Subtraction of a Vector

Match List I ...

Question

Match $List I$ with the $List II$ and select the correct answer using the code given below the lists :

$\begin{matrix} List I & List II (A) & If \to a = t^i - 3^j + 2 t^k, \to b =^i - 2^j + 2^k and \to c = 3^i + t^j -^k, then the & (P) & 1 value of ⎛ ⎜ ⎝ 2 \int 1 \to a \cdot (\to b \times \to c) d t + 2 ⎞ ⎟ ⎠ is equal to (B) & The value of t \in R for which the vectors \to a = (1, - 2, 3), \to b = (- 2, 3, - 4), & (Q) & 2 \to c = (1, - 1, t) form a linearly dependent system is (C) & If the area of the parallelogram whose diagonals are 3^i +^j - 2^k and & (R) & 3^i - 3^j + 4^k is μ \sqrt{3} sq. unit, then the value of μ is (D) & Let \to p =^i +^j, \to q =^i -^j and \to r =^i + 2^j + 3^k . If \to x is a unit vector & (S) & 4 such that \to p \cdot \to x = 0 and \to q \cdot \to x = 0, then | \to r \cdot \to x | is equal to (T) & 5 \end{matrix}$

Which of the following is the only CORRECT combination ?

(C) \to (Q), (D) \to (R)

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

(C) \to (Q), (D) \to (P)

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

(C) \to (R), (D) \to (P)

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

(C) \to (T), (D) \to (R)

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

Open in App

Solution

The correct option is D $(C) \to (T), (D) \to (R)$
$(C)$
$Area = \frac{1}{2} | d_{1} \times d_{2} |$
$= \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 3 & 1 & - 2 1 & - 3 & 4 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣$
$= \frac{1}{2} \sqrt{4 + 196 + 100}$
$= \frac{1}{2} 10 \sqrt{3} = 5 \sqrt{3}$
$\Rightarrow μ = 5$
$(C) \to (T)$

$(D)$
$\to x = λ (\to p \times \to q)$
$\Rightarrow \to x = λ (- 2^k)$
$\Rightarrow 2 | λ | = 1 (∵ | \to x | = 1)$
$\Rightarrow λ = \pm \frac{1}{2}$
$∴ \to x = \pm \to k$
Now, $∣ ∣ \to r \cdot \to x ∣ ∣ = | \pm 3 | = 3$
$(D) \to (R)$

Suggest Corrections

Similar questions

List I

List II

\begin{matrix} List I & List II (A) & If \to a = t^i - 3^j + 2 t^k, \to b =^i - 2^j + 2^k and \to c = 3^i + t^j -^k, then the & (P) & 1 value of ⎛ ⎜ ⎝ 2 \int 1 \to a \cdot (\to b \times \to c) d t + 2 ⎞ ⎟ ⎠ is equal to (B) & The value of t \in R for which the vectors \to a = (1, - 2, 3), \to b = (- 2, 3, - 4), & (Q) & 2 \to c = (1, - 1, t) form a linearly dependent system is (C) & If the area of the parallelogram whose diagonals are 3^i +^j - 2^k and & (R) & 3^i - 3^j + 4^k is μ \sqrt{3} sq. unit, then the value of μ is (D) & Let \to p =^i +^j, \to q =^i -^j and \to r =^i + 2^j + 3^k . If \to x is a unit vector & (S) & 4 such that \to p \cdot \to x = 0 and \to q \cdot \to x = 0, then | \to r \cdot \to x | is equal to (T) & 5 \end{matrix}

List I

List II

\begin{matrix} List I & List II (A) & The possible value of a if \to r = (^i +^j) + λ (^i + 2^j -^k) & (P) & - 4 and \to r = (^i + 2^j) + μ (-^i +^j + a^k) are not consistent, where λ and μ are scalars, is (B) & The angle between vectors \to a = λ^i - 3^j -^k and & (Q) & - 2 \to b = 2 λ^i + λ^j -^k is acute, whereas vector \to b makes an obtuse angle with the axes of coordinates. Then λ can be (C) & The possible value of a such that 2^i -^j +^k, & (R) & 1^i + 2^j + (1 + a)^k and 3^i + a^j + 5^k are coplanar, is (D) & If \to A = 2^i + λ^j + 3^k, \to B = 2^i + λ^j +^k, \to C = 3^i +^j & (S) & 2 and \to A + λ \to B is perpendicular to \to C, then | 2 λ | is (T) & 3 \end{matrix}

If \to a = 2^i + 3^j +^k, \to b =^i - 2^j +^k and \to c = - 3^i +^j + 2^k,

[\to a \to b \to c] .

\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k

\to c = - 2^i +^j - 3^k

\to r = x \to a + y \to b + z \to c

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

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

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

\to v

\to a

\to b

\to c

\frac{1}{\sqrt{3}}

Join BYJU'S Learning Program