1
BITSAT 2022
+3
-1

$$\widehat u$$ and $$\widehat v$$ are two non-collinear unit vectors such that $$\left| {{{\widehat u + \widehat v} \over 2} + \widehat u \times \widehat v} \right| = 1$$. Then the value of $$|\widehat u \times \widehat v|$$ is equal to

A
$$\left| {{{\widehat u + \widehat v} \over 2}} \right|$$
B
$$|\widehat u + \widehat v|$$
C
$$|\widehat u - \widehat v|$$
D
$$\left| {{{\widehat u - \widehat v} \over 2}} \right|$$
2
BITSAT 2021
+3
-1

The points with position vectors $$10\widehat i + 3\widehat j$$, $$12\widehat i - 5\widehat j$$ and $$a\widehat i + 11\widehat j$$ are collinear, if a is

A
$$-$$8
B
4
C
2
D
$${{82} \over 9}$$
3
BITSAT 2021
+3
-1

Let a, b, c be vectors of lengths 3, 4, 5 respectively and a be perpendicular to (b + c), b to (c + a) and c to (a + b), then the value of (a + b + c) is

A
2$$\sqrt5$$
B
2$$\sqrt2$$
C
10$$\sqrt5$$
D
5$$\sqrt2$$
4
BITSAT 2021
+3
-1

For non-zero vectors a, b, c; |(a $$\times$$ b) . c| = |a| |b| |c| holds if and only if

A
a . b = 0, b . c = 0
B
b . c = 0, c . a = 0
C
c . a = 0, a . b = 0
D
a . b = b . c = c . a = 0
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12