class 12

Math

Algebra

Vector Algebra

If the vectors $AB=3i^+4k^$ and $AC=5i^−2j^ +4k^$are the sides of a triangle ABC, then the length of the median through A is

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Three vectors $→a$, $→b$and $→c$satisfy the condition $→a+→b+→c=→0$. Evaluate the quantity $μ=→a→˙b+→b→˙c+→⋅→a$, if $∣→a∣=1,∣→b∣=4$and $∣→c∣=2$.

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∣∣ $.

Write two different vectors having same magnitude.

Find the unit vector in the direction of the vector $a=i^+j^ +2k^$

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

Show that the points $A(2i^−j^ +k^),B(i^−3j^ −5k^),C(3i^−4j^ −4k^)$are the vertices of a right angled triangle.

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.

For any two vectors $a$ and $b$, we always have $∣∣ a+b∣∣ ≤∣a∣+∣∣ b∣∣ $