Class 12

Math

Algebra

Vector Algebra

Write the direction-cosines of the line joining the points (1, 0, 0) and (0, 1, 1).

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For any two vectors $→a$and $→b$we always have $∣→a→˙b∣≤∣→a∣∣→b∣$(Cauchy-Schwartz inequality).

If with reference to the right handed system of mutually perpendicular unit vectors $i^,j^ $and $k^$, $→α=3i^−j^ ,→β=2i^+j^ −3k^$, then express $→β$in the from $→β=→β_{1}+→β_{2}$, where \displaystyle-

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.

Find the projection of the vector $i^−j^ $on the vector $i^+j^ $

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

In triangle ABC (Figure), which of the following is not true: (A) $AB+BC+CA=0$ (B) $AB+BC−AC=0$ (C) $AB+BC−CA=0$ (D) $AB−CB+CA=0$

Find the magnitude of two vectors $a$and $b$having the same magnitude and such that the angle between them is $60_{∘}$and their scalar product is $21 $.

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