edurack

Vector Algebra: JEE Mains 2022 June 29 Shift 2

Medium· Types of vectors and operations· +4 / −1

Let

A

,

B

,

C

be three points whose position vectors respectively are

\vec a=\hat i+4\hat j+3\hat k

,

\vec b=2\hat i+\alpha\hat j+4\hat k

,

\alpha\in\mathbb R

,

\vec c=3\hat i-2\hat j+5\hat k

. If

\alpha

is the smallest positive integer for which

\vec a,\vec b,\vec c

are non-collinear, then the length of the median, in

\triangle ABC

, through

A

is :

Practise more Vector Algebra PYQs

Let a= i-2 j+3 k , b= i+ j+ k and c be a vector such that a+( b× c)= 0 and b· c=5 . Then the value of 3( c· a) is equal to ______.
JEE Mains 2022 June 29 Shift 2 · Hard
Let a=2 i+ j+3 k , b=3 i+3 j+ k and c=c_1 i+c_2 j+c_3 k . If a, b, c are coplanar, a· c=5 and b is perpendicular to c , find…
JEE Mains 2022, June 28 - Shift 1 · Hard
Let a=α i+3 j- k , b=3 i-β j+4 k and c= i+2 j-2 k where α,β R , be three vectors. If the projection of a on c is 103 and b× c=-6 i+10 j+7…
JEE Mains 2022 June 29 Shift 1 · Easy