Match List I with List II
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LIST I |
LIST II |
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A. The area of parallelogram determined by vectors $2\hat i$ and $3\hat j$ |
I. 2 |
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B. The value of $(\hat i×\hat j)·\hat k+(\hat j×\hat k)·\hat i$ |
II. 4 |
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C. The value of a for which the vectors $2\hat i-3\hat j+4\hat k$ and $a\hat i -6\hat j +8\hat k$ are collinear. |
III. 0 |
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D. The value of λ for which the vectors $2\hat i+\hat j+\hat k$ and $2\hat i-4\hat j+λ\hat k$ are perpendicular |
IV. 6 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
(A) area = $|2\hat i ×3\hat j|$ = 6 sq. units
(B) $(\hat i×\hat j)·\hat k+(\hat j×\hat k)·\hat i=\hat k.\hat k+\hat i.\hat i=1+1=2$
(C) $2\hat i-3\hat j+4\hat k$ and $a\hat i -6\hat j +8\hat k$ are collinear
$⇒\frac{2}{a}=\frac{4}{8}⇒9=4$
(D) $(2\hat i+\hat j+\hat k).(2\hat i-4\hat j+λ\hat k)=0$
$⇒4-4+λ=0⇒λ=0$