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1.

The vectors `vec(a), vec(b),vec(c )` are of same magnitude and taken pariwise , they contain equal angles. If `vec(a) = hat(i) +hat(j) , vec(b) = hat(j) + hat(k) ` then the vector `vec(c )` =A. ` hat (i) + hat (k)`B. `hat(i) + 2hat(j) + 3 hat (k)`C. ` - hat(i) + hat(j) + 2hat(k) `D. ` -1/3i + 4/3 hat(j)-1/3hat(k)`

Answer» Correct Answer - A,D
Discussion
2.

If `vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec(b) = hat (i) + hat (j) - hat (k) and |vec (a) xx vec(b)| = sqrt(13 m )` then the value of m is -A. 3B. 4C. 2D. 1

Answer» Correct Answer - c
Discussion
3.

If the vectors `vec(a) = 3 hat (j) + 6 hat (k) and vec (b) = - 2 hat (i) + m hat (j) - 3 hat (k) ` are perpendicular to each other , then the value of m is -A. 12B. `-6`C. `-12`D. 6

Answer» Correct Answer - c
Discussion
4.

f `vec(a)` is any vector , then -A. ` (vec(a).hat(i))hat(i)+(vec(a).hat(j)) hat(j) + (veca.hat(k))hat(k) = vec(a)`B. ` (vec(a).hat(i))^(2)+(vec(a).hat(j)) ^(2)+ (vec(a) . hat(k))^(2)= |vec(a)|^(2)`C. ` hat (i)xx (vec(a)xx hat(j)) + hat(j) (vec(a) xx hat(j))+ hat(k) xx (vec(a)xxvec(k)) = 2 vec(a)`D. all of the above

Answer» Correct Answer - A,B,C,D
Discussion
5.

If ` vec (a)= 2 hat (i) - hat (j) + hat (k) and vec(b) = - hat (i) + 3 hat (j) + 4 hat (k) ` , then value of ` vec (a). vec(b) ` is -A. 1B. 3C. `-3`D. `-1`

Answer» Correct Answer - d
Discussion
6.

Let `vec(a), vec(b),vec(c)` be three non - coplanar vectors where ` vec(a) xx vec(b)xx vec(c), vec(beta) = vec(c ) xx vec(a) andvec(gamma) = vec(a) xx vec(b) ` ` [ vec(beta) xx vec(gamma) , vec(gamma) xx vec(alpha) , vec(alpha) xx vec(beta)] ` `[ vec(beta) xx vec(gamma) , vec(gamma) xx vec alpha , vec (alpha) xx vec(beta) ] ` is equal to -A. ` [ vec(a)" " vec (b) " "vec(c ) ] `B. `[ vec(a)" "vec(b)" " vec(c ) ]^(2)`C. ` [ vec(a)" " vec(b)" " vec(c)]^(4) `D. 0

Answer» Correct Answer - c
Discussion
7.

Let `vec(a), vec(b),vec(c)` be three non - coplanar vectors where ` vec(a) xx vec(b)xx vec(c), vec(beta) = vec(c ) xx vec(a) andvec(gamma) = vec(a) xx vec(b) ` ` [ vec(beta) xx vec(gamma) , vec(gamma) xx vec(alpha) , vec(alpha) xx vec(beta)] ` ` vec(alpha) xx vec(beta) . vec(gamma) ` is equal to -A. ` [ vec(a)" " vec(b)" " vec(c )] `B. ` [ vec(a) " " vec(b)" " vec(c)] ^(2)`C. ` [ vec(a)" " vec(b)" " vec(c)] ^(4)`D. 0

Answer» Correct Answer - b
Discussion