Class 12

Math

Algebra

Vector Algebra

Find a unit vector perpendicular to each of the vector $a+b$and $a−b$ where $a=3i^+2j^ +2k^$ and $b=i^+2j^ −2k^$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

For given vector, $a$ = 2$i^$ $j$ +2$k^$ and $b$ = -$i^$ +$j^ $ - $k^$ , find the unit vector in the direction of the vector $a$ +$b$ .

$A,B,CandD$ have position vectors $a,b,candd,$ respectively, such that $a−b=2(d−c)˙$ Then a. $ABandCD$ bisect each other b. $BDandAC$ bisect each other c. $ABandCD$ trisect each other d. $BDandAC$ trisect each other

Three coinitial vectors of magnitudes a, 2a and 3a meet at a point and their directions are along the diagonals if three adjacent faces if a cube. Determined their resultant R. Also prove that the sum of the three vectors determinate by the diagonals of three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube.

If $α+β +γ =aδandβ +γ +δ=bα,αandδ$ are non-colliner, then $α+β +γ +δ$ equals a. $aα$ b. $bδ$ c. $0$ d. $(a+b)γ $

For any four vectors, prove that $(b×c)a×d˙ +(c×a)b×d˙ +(a×b)c×d˙ =0.$

In a trapezium, vector $BC=αAD˙$ We will then find that $p =AC+BD$ is collinear with$AD˙$ If $p =μAD,$ then which of the following is true? a. $μ=α+2$ b. $μ+α=2$ c. $α=μ+1$ d. $μ=α+1$

Points $A(a),B(b),C(c)andD(d)$ are relates as $xa+yb+zc+wd=0$ and $x+y+z+w=0,wherex,y,z,andw$ are scalars (sum of any two of $x,y,znadw$ is not zero). Prove that if $A,B,CandD$ are concylic, then $∣xy∣∣∣ a−b∣∣ _{2}=∣wz∣∣∣ c−d∣∣ _{2}˙$

Let $D,EandF$ be the middle points of the sides $BC,CAandAB,$ respectively of a triangle $ABC˙$ Then prove that $AD+BE+CF=0$ .