class 12

Math

Algebra

Vector Algebra

Let $a,b,andc$ be three non coplanar unit vectors such that the angle between every pair of them is $3π $. If $a×b+b×x=pa+qb+rc$ where p,q,r are scalars then the value of $q_{2}p_{2}+2q_{2}+r_{2} $ is

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

Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).

If $a,b,c$are mutually perpendicular vectors of equal magnitudes, show that the vector $a+b+c$is equally inclined to $a,b$ and $c$.

If either $a=0$or $b=0$, then $a⋅b=0$But the converse need not be true. Justify your answer with an example.

Find angle $θ$between the vectors $a=i^+j^ −k^$and $b=i^−j^ +k^$.

Write the direction ratios of the vector $→a=i^+j^ −2k^$and hence calculate its direction cosines.

Find the vector joining the points $P(2,3,0)$and $Q(1,2,4)$directed from P to Q.

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