Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

Match List I with List II

LIST I

LIST II

A. The area of parallelogram determined by vectors $2\hat i$ and $3\hat j$

I. 2

B. The value of $(\hat i×\hat j)·\hat k+(\hat j×\hat k)·\hat i$

II. 4

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

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:

Options:

A-I, B-II, C-III, D-IV

A-II, B-I, C-III, D-IV

A-III, B-IV, C-II, D-I

A-IV, B-I, C-II, D-III

Correct Answer:

A-IV, B-I, C-II, D-III

Explanation:

(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) $(2\hat i+\hat j+\hat k).(2\hat i-4\hat j+λ\hat k)=0$

$⇒4-4+λ=0⇒λ=0$