Linear Combination of Vectors
Trending Questions
Q. Let, →a=^i+2^j+^k, →b=^i−^j+^k, →c=^i+^j−^k.
A vector coplanar to →a and →b has a projection along →c of magnitude 1√3, then the vector is
A vector coplanar to →a and →b has a projection along →c of magnitude 1√3, then the vector is
- 4^i−^j+4^k
- 4^i+^j−4k
- 2^i+^j+^k
- None of these
Q. Two unit vectors →a and →b are pependicular to each other. Another unit vector →c is inclined at an angle α to both →a and →b. If →c=x→a+y→b+z(→a×→b), then
- x2+y2=1
- x2=y2
- z2=−cos2α
- x2+y2+z2=1
Q. If →v1and→v2 are two vectors in x – y plane. Then any vector in that plane can be obtained by the linear combination of these two vectors.The statement is
- True
- False
Q. What will be the magnitude of the vector →V, which is the sum of 3 times the vector →A=2ˆi+2ˆj−6ˆk and −2 times the vector →B=6ˆi−3ˆj−11ˆk
- 14
- 18
- 12
- 16
Q. Let, →a=^i+2^j+^k, →b=^i−^j+^k, →c=^i+^j−^k.
A vector coplanar to →a and →b has a projection along →c of magnitude 1√3, then the vector is
A vector coplanar to →a and →b has a projection along →c of magnitude 1√3, then the vector is
- 4^i−^j+4^k
- 4^i+^j−4k
- 2^i+^j+^k
- None of these
Q. The linear combination of ¯a=[12]and¯b=[03] which gives the vector [22] will be ___ ¯a +__ ¯b. (If any of the blanks is a fraction, enter the value to the nearest hundredth place).
Q. Let →a=^i+^j; →b=2^i−^k. Then, vector →r satisfying the equations →r×→a=→b×→a and →r×→b=→a×→b is
- ^i−^j+3^k
- 3^i−^j+^k
- 3^i+^j−^k
- ^i−^j−^k
Q. Let →a=2→i+^j+^k, →b=^i+2^j−^k and a unit vector →c be coplanar. If →c is perpendicular to →a, then →c is equal to
- 1√2(−^j+^k)
- 1√3(−^i−^j−^k)
- 1√5(−^i−2^j)
- 1√5(^i−^j−^k)
