class 12

Math

Algebra

Vector Algebra

In a $ΔABC,∠A+∠B=120_{∘},a=3 +1,b=3 −1$, then the ratio of $∠A$ to $∠B$ is (a) $7:1$ (b) $5:1$ (c) $3:1$ (d) $5:3$

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Consider two points P and Q with position vectors $→OP=3→a−2→b$and $→OQ=→a+→b$Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, (i) internally, and (ii) externally.

Find the value of x for which $x(i^+j^ +k^)$is a unit vector.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are $2(a+b)$and $(a−3b)$externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

Write all the unit vectors in $XY−plane˙$

If $θ$ is the angle between two vectors $a$and $b$, then $a⋅b≥0$only when(A) $0<θ<2π $ (B) $0≤θ≤2π $ (C) $0<θ<π$ (D) 0

Find the sum of the vectors $a=i^−2j^ +k^$ , $b=−2i^+4j^ +5k^$ and $c=i^−6j^ −7k^$

Let $a,b$and $c$be three vectors such that $∣a∣=3,∣∣ b∣∣ =4,∣c∣=5$and each one of them being perpendicular to the sum of the other two, find $∣∣ a+b+c∣∣ $.

Find $∣a∣$and $∣∣ b∣∣ $, if $(a+b)(a−b)˙ =8$and $∣a∣=8∣∣ b∣∣ $