Class 12

Math

Algebra

Vector Algebra

If $a=2i^−3j^ +k^,b^=−i^+k^,c=2j^ −k^$are three vectors, find the area of the parallelogram having diagonals $(a+b)$and $(b+c)˙$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

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

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 $m/s_{2}$

Evaluate the product $(3a−5b)⋅(2a+7b)$

Show that the points A, B and C with position vectors, $a=3i^−4j^ −4k^$, $b=2i^−j^ +k^$and $c=i^−3j^ −5k^$ respectively form the vertices of a right angled triangle.

Write two different vectors having same direction.

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

A girl walks 4 km towards west, then she walks 3 km in a direction $30o$east of north and stops. Determine the girls displacement from her initial point of departure.

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.