Class 12

Math

Algebra

Vector Algebra

Show that the points A, B and C with position vectors, $a=3i^−4j^ −4k^$, $b=2i^−j^ +k^$and $c=i^−3j^ −5k^$ respectively form the vertices of a right angled triangle.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

$ABCD$ parallelogram, and $A_{1}andB_{1}$ are the midpoints of sides $BCandCD,$ respectivley . If $∀_{1}+AB_{1}=λAC,thenλ$ is equal to a. $21 $ b. $1$ c. $23 $ d. $2$ e. $32 $

Two forces $AB$ and $AD$ are acting at vertex A of a quadrilateral ABCD and two forces $CB$ and $CD$ at C prove that their resultant is given by 4$EF$ , where E and F are the midpoints of AC and BD, respectively.

If $A(−4,0,3)andB(14,2,−5),$ then which one of the following points lie on the bisector of the angle between $OAandOB(O$ is the origin of reference )? a. $(2,2,4)$ b. $(2,11,5)$ c. $(−3,−3,−6)$ d. $(1,1,2)$

If $a,b,candd$ are four vectors in three-dimensional space with the same initial point and such that $3a−2b+c−2d=0$ , show that terminals $A,B,CandD$ of these vectors are coplanar. Find the point at which $ACandBD$ meet. Find the ratio in which $P$ divides $ACandBD˙$

Find a vector magnitude 5 units, and parallel to the resultant of the vectors $a=2i^+3j^ −k^$ and $b=i^−2j^ +k^˙$

A man travelling towards east at 8km/h finds that the wind seems to blow directly from the north On doubling the speed, he finds that it appears to come from the north-east. Find the velocity of the wind.

If $a,b,andc$ are mutually perpendicular vectors and $a=α(a×b)+β(b×c)+γ(c×a)and[abc]=1,$ then find the value of $α+β+γ˙$

If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.