Class 12

Math

Algebra

Vector Algebra

$A,B,CandD$ 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

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Fined the unit vector in the direction of vector $PQ$ , where $P$ and $Q$ are the points (1,2,3) and (4,5,6), respectively.

If two side of a triangle are $i^+2j^ andi^+k^$ , then find the length of the third side.

The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

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.

Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

If $aandb$ are two unit vectors and $θ$ is the angle between them, then the unit vector along the angular bisector of $a$ and $b$ will be given by a. $cos(θ/2)a−b $ b. $2cos(θ/2)a+b $ c. $2cos(θ/2)a−b $ d. none of these

ABC is a triangle and P any point on BC. if $PQ$ is the sum of $AP$ + $PB$ +$PC$ , show that ABPQ is a parallelogram and Q , therefore , is a fixed point.

A pyramid with vertex at point $P$ has a regular hexagonal base $ABCDEF$ , Positive vector of points A and B are $i^andi^+2j^ $ The centre of base has the position vector $i^+j^ +3 k^˙$ Altitude drawn from $P$ on the base meets the diagonal $AD$ at point $G˙$ find the all possible position vectors of $G˙$ It is given that the volume of the pyramid is $63 $ cubic units and $AP$ is 5 units.