The vector, d\(\overset { \wedge }{ i } +\overset { \wedge }{ j } +2\overset { \wedge }{ k } ,\overset { \wedge }{ i } +\lambda \overset { \wedge }{ j } -\overset { \wedge }{ k } \) t and \(2\overset { \wedge }{ i } -\overset { \wedge }{ j } +\lambda \overset { \wedge }{ k } \) are co-planar if _____________

(a)

λ = -2

(b)

λ = 1+\(\sqrt { 3 } \)

(c)

λ = 1 - \(\sqrt { 3 } \)

(d)

λ = -2,1土 \(\sqrt { 3 } \)

If  \(\left| \overset { \rightarrow }{ a } \right| =\left| \overset { \rightarrow }{ b } \right| =1\)such that \(\overset { \rightarrow }{ a } +2\overset { \rightarrow }{ b } \) and \(5\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \) are perpendicular to each other, then the angle between \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) is _______________

(a)

45^o

(b)

60^o

(c)

cos^-1 \(\left( \frac { 1 }{ 3 } \right) \)

(d)

cos^-1 \(\left( \frac { 2 }{ 7 } \right) \)

The p.v, OP of a point P make angles 60^o and 45^o with X and Y axis respectively. The angle of inclination of  \(\overset { \rightarrow }{ OP } \) with z-axis is ___________

(a)

75^o

(b)

60^o

(c)

45^o

(d)

3

The value of \({ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }\) is _____________

(a)

\(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

(b)

4 \(\overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \)

(c)

\(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }-{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

(d)

4 \({ \left| \overset { \rightarrow }{ a } \right| }^{ 2 }{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 }\)

The two planes 3x + 3y - 3z - 1 = 0 and x + y - z + 5 = 0 are _____________

(a)

mutually perpendicular

(b)

parallel

(c)

inclined at 45^o

(d)

inclined at 30