Vector Algebra

JEE Main 2024 (Online) 29th January Evening ShiftMCQMedium📈 Topic in 59% papers+4−1

Ques. 1JEE Main 2024, 29 January (Evening Shift)

Let OA= a, OB=12 a+4 b and OC= b, where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then area of the quadrilateral OABCarea of S is equal to .

Answer

(3) 8

Solution

[figure]

Area of S =| a b|

∵ Diagonal OB splits OABC into OAB and OBC:

Area(OABC) = 12| a (12 a+4 b)|+ 12|(12 a+4 b) b|

= 12(4| a b|)+ 12(12| a b|) ( a a= b b= 0)

=8| a b|

Ratio = 8| a b|| a b|=8

Answer: (3)

Keep practising — Vector Algebra

Ques. 2JEE Main 2024, 27 January (Morning Shift)

Let a= i+2 j+ k, b=3( i- j+ k). Let c be the vector such that a c= b and a c=3. Then a (( c b)- b- c) is equal to :

Ques. 3JEE Main 2024, 27 January (Morning Shift)

The least positive integral value of , for which the angle between the vectors i-2 j+2 k and i+2 j-2 k is acute, is .

Ques. 4JEE Main 2024, 27 January (Evening Shift)

The position vectors of the vertices A, B and C of a triangle are 2 i-3 j+3 k, 2 i+2 j+3 k and - i+ j+3 k respectively. Let l denote the length of the angle bisector AD of where D is on the line segment BC, then 2l2 equals :

All Vector Algebra PYQs →

PDFDownload Vector Algebra PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)