The value of -a- for which the vectorsA -2 i -3 j -3 kB -3 i - a -7 kC -5 i -3 j -6 kare coplanar is

For the vectors to be coplanar, their box product should be zero. 2 333a 7536=0 Now solving the determinant 2(a×6 ( 7)×3) ( 3)(3×6 5×( 7) nbsp; nbsp; nbsp ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Scalar Triple Product

The value of ...

Question

The value of 'a' for which the vectors
A=2i-3j+3k
B=3i+aj-7k
C=5i+3j+6k
are coplanar is

Open in App

Solution

For the vectors to be coplanar, their box product should be zero.
$⎛ ⎜ ⎝ \begin{matrix} 2 & - 3 & 3 3 & a & - 7 5 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣ = 0$
Now solving the determinant
$2 (a \times 6 - (- 7) \times 3) - (- 3) (3 \times 6 - 5 \times (- 7) + 3 (3 \times 3 - 5 \times a) = 0 ∴ a = 76$

Suggest Corrections

Similar questions

Q. The value of 'a' for which the vectors
A=2i-3j+3k
B=3i+aj-7k
C=5i+3j+6k
are coplanar is

Q. Which of the following unit vector is coplanar with vectors

\to A = 2 ˆ i - 3 ˆ j + ˆ k and \to B = 3 ˆ i - ˆ j - 3 ˆ k

and orthogonal to the vector

\to C = 8 ˆ i - 5 ˆ j + 2 ˆ k

Q. The value of n so that vectors

2 ˆ i + 3 ˆ j - 2 ˆ k, 5 ˆ i + n ˆ j + ˆ k and - ˆ i + 2 ˆ j + 3 ˆ k

may be coplanar find the value ?

Q. The value of 'a' for which the vectors
A=2i-j-4k ,
B=i-5j+ak and
C=2i+3j+4k are linearly dependent is

Join BYJU'S Learning Program

The value of 'a' for which the vectors A=2i-3j+3k B=3i+aj-7k C=5i+3j+6k are coplanar is

For the vectors to be coplanar, their box product should be zero. ⎛⎜⎝2−333a−7536∣∣ ∣∣=0 Now solving the determinant 2(a×6−(−7)×3)−(−3)(3×6−5×(−7) +3(3×3−5×a)=0∴ a = 76

The value of 'a' for which the vectors
A=2i-3j+3k
B=3i+aj-7k
C=5i+3j+6k
are coplanar is