Class 12

Math

Algebra

Vector Algebra

Classify the following measures as scalars and vectors.(i) 10 kg (ii) 2 meters north-west (iii) $40_{∘}$(iv) 40 watt (v) $10_{−19}$ coulomb (vi)20 $m/s_{2}$

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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.

If the projections of vector $a$ on $x$ -, $y$ - and $z$ -axes are 2, 1 and 2 units ,respectively, find the angle at which vector $a$ is inclined to the $z$ -axis.

if $Ao$ + $OB$ = $BO$ + $OC$ ,than prove that B is the midpoint of AC.

If $a,b$ are two non-collinear vectors, prove that the points with position vectors $a+b,a−b$ and $a+λb$ are collinear for all real values of $λ˙$

If in parallelogram ABCD, diagonal vectors are $AC=2i^+3j^ +4k^$ and $BD=−6i^+7j^ −2k^,$ then find the adjacent side vectors $AB$ and $AD$

The position vectors of the point $A,B,CandDare3i^−2j^ −k^,2i^+3j^ −4k^,−i^+j^ +2k^$ and 4$i^+5j^ +λk^,$ respectively. If the points $A,B,CandD$ lie on a plane, find the value of $λ˙$

In a quadrilateral $PQRS,PQ=a,Q R,b,SP=a−b,M$ is the midpoint of $Q RandX$ is a point on $SM$ such that $SX=54 SM˙$ Prove that $P,XandR$ are collinear.

Find the point of intersection of AB and $A($ 6,-7,0),B(16,-19,-4,) , C(0,3,-6) and D(2,-5,10).