Class 12

Math

Algebra

Vector Algebra

Find the resultant of two velocities 6 km/hr and $62 $km/hr inclined to one another at an angle of 135.

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If $a$ is a unit vector and $(x−a).(x+a)=8$, then find $∣x∣$

The scalar product of the vector $i^+j^ +k^$with a unit vector along the sum of vector $2i^+4j^ −5k^$and $λi^+2j^ +3k^$is equal to one. Find the value of $λ$.

In Figure, which of the vectors are: (i) Collinear (ii) Equal (iii) Coinitial

Find the unit vector in the direction of the sum of the vectors, $→a=2i^+2j^ −5k^$and $→b=2i^+j^ +3k^$.

Show that each of the given three vectors is a unit vector: $71 (2i^+3j^ +6k^),71 (3i^−6j^ +2k^),71 (6i^+2j^ −3k^)$Also, show that they are mutually perpendicular to each other.

Find the direction cosines of the vector joining the points $A(1,2,3)$and$B(1,2,1)$, directed from A to B.

Let $a=i^+4j^ +2k^,b=3i^−2j^ +7k^$and $c=2i^−j^ +4k^$. Find a vector $d$which is perpendicular to both $a$and $b$and $c$. $d=15$.

Find the scalar components and magnitude of the vector joining the points $P(x_{1},y_{1},z_{1})$and $Q(x_{2},y_{2},z_{2})$