Vector Algebra

JEE Main 2025 (Online) 23rd January Morning ShiftMCQMedium📈 Topic in 8% papers+4−1

Ques. 1JEE Main 2025, 23 January (Morning Shift)

Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC, divides the arc AC such that length of arc ABlength of arc BC= 15, and OC= OA+ OB, then + 2( 3-1) is equal to

2 3
5 3
2+ 3
2- 3

Answer

(4) 2- 3

Solution

Arcs are in the ratio of the angles at the centre (1 : 5): AOB=15 , BOC=75

[figure]

Unit circle: OA=(1,0), OB=( 15 , 15 ), OC=(0,1)

y: 1= 15 = 6+ 2; x: 0= + 15 =-(2+ 3)

2( 3-1) =( 3-1)(2 3+2)=4

+ 2( 3-1) =2- 3

Answer: (4)

Keep practising — Vector Algebra

Ques. 2JEE Main 2025, 23 January (Evening Shift)

Let the point A divide the line segment joining the points P(-1,-1,2) and Q(5,5,10) internally in the ratio r:1 (r>0). If O is the origin and ( OQ OA )- 15 | OP OA |2=10, then the value of r is :

Ques. 3JEE Main 2025, 22 January (Morning Shift)

Let c be the projection vector of b= i+4 k, >0, on the vector a= i+2 j+2 k. If | a+ c|=7, then the area of the parallelogram formed by the vectors b and c is .

Ques. 4JEE Main 2025, 22 January (Evening Shift)

Let a and b be two unit vectors such that the angle between them is 3. If a+2 b and 3 a- b are perpendicular to each other, then the number of values of in [-1,3] is :

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